Relevant bibliographies by topics / Lyapunov stability

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Lyapunov stability'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 November 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Lyapunov stability.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Lyapunov stability"

1

Lakshmikantham, V., X. Liu, and S. Leela. "Variational Lyapunov method and stability theory." Mathematical Problems in Engineering 3, no. 6 (1998): 555–71. http://dx.doi.org/10.1155/s1024123x97000689.

Full text
Abstract:
By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.
APA, Harvard, Vancouver, ISO, and other styles
2

Ates, Muzaffer, and Nezir Kadah. "Novel stability and passivity analysis for three types of nonlinear LRC circuits." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, no. 2 (July 31, 2021): 227–37. http://dx.doi.org/10.11121/ijocta.01.2021.001073.

Full text
Abstract:
In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.
APA, Harvard, Vancouver, ISO, and other styles
3

Bomze, Immanuel M., and Jörgen W. Weibull. "Does Neutral Stability Imply Lyapunov Stability?" Games and Economic Behavior 11, no. 2 (November 1995): 173–92. http://dx.doi.org/10.1006/game.1995.1048.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Justus, James. "Ecological and Lyapunov Stability*." Philosophy of Science 75, no. 4 (October 2008): 421–36. http://dx.doi.org/10.1086/595836.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Ledrappier, F., and L. S. Young. "Stability of Lyapunov exponents." Ergodic Theory and Dynamical Systems 11, no. 3 (September 1991): 469–84. http://dx.doi.org/10.1017/s0143385700006283.

Full text
Abstract:
AbstractWe consider small random perturbations of matrix cocycles over Lipschitz homeomorphisms of compact metric spaces. Lyapunov exponents are shown to be stable provided that our perturbations satisfy certain regularity conditions. These results are applicable to dynamical systems, particularly to volume-preserving diffeomorphisms.
APA, Harvard, Vancouver, ISO, and other styles
6

Kunitsyn, A. L., and V. N. Tkhai. "Stability in Lyapunov systems." Journal of Applied Mathematics and Mechanics 70, no. 4 (January 2006): 497–503. http://dx.doi.org/10.1016/j.jappmathmech.2006.09.003.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Liu, Yunping, Xijie Huang, Yonghong Zhang, and Yukang Zhou. "Dynamic Stability and Control of a Manipulating Unmanned Aerial Vehicle." International Journal of Aerospace Engineering 2018 (June 12, 2018): 1–13. http://dx.doi.org/10.1155/2018/3481328.

Full text
Abstract:
This paper focuses on the dynamic stability analysis of a manipulator mounted on a quadrotor unmanned aerial vehicle, namely, a manipulating unmanned aerial vehicle (MUAV). Manipulator movements and environments interaction will extremely affect the dynamic stability of the MUAV system. So the dynamic stability analysis of the MUAV system is of paramount importance for safety and satisfactory performance. However, the applications of Lyapunov’s stability theory to the MUAV system have been extremely limited, due to the lack of a constructive method available for deriving a Lyapunov function. Thus, Lyapunov exponent method and impedance control are introduced, and the Lyapunov exponent method can establish the quantitative relationships between the manipulator movements and the dynamics stability, while impedance control can reduce the impact of environmental interaction on system stability. Numerical simulation results have demonstrated the effectiveness of the proposed method.
APA, Harvard, Vancouver, ISO, and other styles
8

Yunping, Liu, Wang Lipeng, Mei Ping, and Hu Kai. "Stability Analysis of Bipedal Robots Using the Concept of Lyapunov Exponents." Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/546520.

Full text
Abstract:
The dynamics and stability of passive bipedal robot have an important impact on the mass distribution, leg length, and the angle of inclination. Lyapunov’s second method is difficult to be used in highly nonlinear multibody systems, due to the lack of constructive methods for deriving Lyapunov fuction. The dynamics equation is established by Kane method, the relationship between the mass, length of leg, angle of inclination, and stability of passive bipedal robot by the largest Lyapunov exponent. And the Lyapunov exponents of continuous dynamical systems are estimated by numerical methods, which are simple and easy to be applied to the system stability simulation analysis, provide the design basis for passive bipedal robot prototype, and improve design efficiency.
APA, Harvard, Vancouver, ISO, and other styles
9

Beisenbi, Мamyrbek, and Samal Kaliyeva. "Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions." Eastern-European Journal of Enterprise Technologies 1, no. 3 (121) (February 28, 2023): 6–14. http://dx.doi.org/10.15587/1729-4061.2023.274063.

Full text
Abstract:
One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements
APA, Harvard, Vancouver, ISO, and other styles
10

Kostrub, Irina Dmitrievna. "HURWITZ MATRIX, LYAPUNOV AND DIRICHLET ON THE SUSTAINABILITY OF LYAPUNOV’S." Tambov University Reports. Series: Natural and Technical Sciences, no. 123 (2018): 431–36. http://dx.doi.org/10.20310/1810-0198-2018-23-123-431-436.

Full text
Abstract:
The concepts of Hurwitz, Lyapunov and Dirichlet matrices are introduced for the convenience of the stability of linear systems with constant coefficients. They allow us to describe all the cases of interest in the stability theory of linear systems with constant coefficients. A similar classification is proposed for systems of linear differential equations with periodic coefficients. Monodromy matrices of such systems can be either Hurwitz matrices or Lyapunov matrices or Dirichlet matrices (in the discrete sense) in a stable case. The new material relates to systems with variable coefficients.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Lyapunov stability"

1

Gumus, Mehmet. "ON THE LYAPUNOV-TYPE DIAGONAL STABILITY." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1421.

Full text
Abstract:
In this dissertation we study the Lyapunov diagonal stability and its extensions through partitions of the index set {1,...,n}. This type of matrix stability plays an important role in various applied areas such as population dynamics, systems theory and complex networks. We first examine a result of Redheffer that reduces Lyapunov diagonal stability of a matrix to common diagonal Lyapunov solutions on two matrices of order one less. An enhanced statement of this result based on the Schur complement formulation is presented here along with a shorter and purely matrix-theoretic proof. We develop a number of extensions to this result, and formulate the range of feasible common diagonal Lyapunov solutions. In particular, we derive explicit algebraic conditions for a set of 2 x 2 matrices to share a common diagonal Lyapunov solution. In addition, we provide an affirmative answer to an open problem concerning two different necessary and sufficient conditions, due to Oleng, Narendra, and Shorten, for a pair of 2 x 2 matrices to share a common diagonal Lyapunov solution. Furthermore, the connection between Lyapunov diagonal stability and the P-matrix property under certain Hadamard multiplication is extended. Accordingly, we present a new characterization involving Hadamard multiplications for simultaneous Lyapunov diagonal stability on a set of matrices. In particular, the common diagonal Lyapunov solution problem is reduced to a more convenient determinantal condition. This development is based upon a new concept called P-sets and a recent result regarding simultaneous Lyapunov diagonal stability by Berman, Goldberg, and Shorten. Next, we consider various types of matrix stability involving a partition alpha of {1,..., n}. We introduce the notions of additive H(alpha)-stability and P_0(alpha)-matrices, extending those of additive D-stability and nonsingular P_0-matrices. Several new results are developed, connecting additive H(alpha)-stability and the P_0(alpha)-matrix property to the existing results on matrix stability involving alpha. We also point out some differences between these types of matrix stability and the conventional matrix stability. Besides, the extensions of results related to Lyapunov diagonal stability, D-stability, and additive D-stability are discussed. Finally, we introduce the notion of common alpha-scalar diagonal Lyapunov solutions over a set of matrices, which is a generalization of common diagonal Lyapunov solutions. We present two different characterizations of this new concept based on the well-known results for Lyapunov alpha-scalar stability [34]. The first one hinges on a general version of the theorem of the alternative, and the second one using Hadamard multiplications stems from an extension of the P-set property. Several illustrative examples and an application concerning a set of block upper triangular matrices are provided.
APA, Harvard, Vancouver, ISO, and other styles
2

Feng, Xiangbo. "Lyapunov exponents and stability of linear stochastic systems." Case Western Reserve University School of Graduate Studies / OhioLINK, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=case1054928844.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Grünvogel, Stefan Michael. "Lyapunov spectrum and control sets." Augsburg [Germany] : Wissner-Verlag, 2000. http://catalog.hathitrust.org/api/volumes/oclc/45796984.html.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Della, rossa Matteo. "Non smooth Lyapunov functions for stability analysis of hybrid systems." Thesis, Toulouse, INSA, 2020. http://www.theses.fr/2020ISAT0004.

Full text
Abstract:
La Nature, dans ses multiples manifestations, nous fournit un grand nombre d’exemples pour lesquels il est nécessaire d’aller au-delà de la distinction classique entre modèles où le temps est décrit comme une entité continue et modèles où le temps est discret/discrétisé. En particulier, pour une multitude de systèmes en physique/ingénierie, ces deux aspects temporels sont fondamentalement liés, et nécessitent donc que ces deux paradigmes soient connectés et mis en relation, pour une meilleure précision et fidélité dans la représentation du phénomène. Cette famille de systèmes est souvent appelée ``systèmes hybrides’’, et différentes formalisations mathématiques ont été proposées.L’objectif de cette thèse est l’analyse et l’étude de la stabilité (asymptotique) pour certaines classes de systèmes hybrides, en proposant des conditions suffisantes à la Lyapunov. Plus spécifiquement, nous nous concentrerons sur des fonctions de Lyauponv non-lisses ; pour cette raison, les premiers chapitres de cette thèse peuvent être considérés comme une introduction générale de ce sujet, proposant les instruments nécessaires issus de l’analyse non-lisse.Tout d'abord, grâce à ces outils, nous pourrons étudier une classe de fonctions de Lyapunov construites par morceaux, avec une attention particulière aux propriétés de continuité des inclusions différentielles qui composent le système hybride considéré. Nous proposons des conditions qui doivent être vérifiées seulement sur un sous-ensemble dense, et donc allant au-delà de résultats existants.En négligeant les hypothèses de continuité, nous étudions ensuite comment les notions de dérivées généralisées se spécialisent en considérant des fonctions construites comme combinaisons de maximum/ minimum de fonctions lisses. Cette structure devient particulièrement fructueuse quand on regarde la classe des systèmes à commutation dépendant de l’état du système. Dans le cas où les sous-dynamiques sont linéaires, nous étudions comment les conditions proposées peuvent être vérifiées algorithmiquement.L’utilité des notions de dérivées généralisées est finalement explorée dans le contexte de la stabilité entrée-état (ISS) pour inclusions différentielles avec perturbations extérieures. Ces résultats nous permettent de proposer des critères de stabilité pour systèmes interconnectés, et notamment une application du synthèse de contrôleurs pour systèmes à commutation dépendant de l’état
Modeling of many phenomena in nature escape the rather common frameworks of continuous-time and discrete-time models. In fact, for many systems encountered in practice, these two paradigms need to be intrinsically related and connected, in order to reach a satisfactory level of description in modeling the considered physical/engineering process.These systems are often referred to as hybrid systems, and various possible formalisms have appeared in the literature over the past years.The aim of this thesis is to analyze the stability of particular classes of hybrid systems, by providing Lyapunov-based sufficient conditions for (asymptotic) stability. In particular, we will focus on non-differentiable locally Lipschitz candidate Lyapunov functions. The first chapters of this manuscript can be considered as a general introduction of this topic and the related concepts from non-smooth analysis.This will allow us to study a class of piecewise smooth maps as candidate Lyapunov functions, with particular attention to the continuity properties of the constrained differential inclusion comprising the studied hybrid systems. We propose ``relaxed'' Lyapunov conditions which require to be checked only on a dense set and discuss connections to other classes of locally Lipschitz or piecewise regular functions.Relaxing the continuity assumptions, we then investigate the notion of generalized derivatives when considering functions obtained as emph{max-min} combinations of smooth functions. This structure turns out to be particularly fruitful when considering the stability problem for differential inclusions arising from regularization of emph{state-dependent switched systems}.When the studied switched systems are composed of emph{linear} sub-dynamics, we refine our results, in order to propose algorithmically verifiable conditions.We further explore the utility of set-valued derivatives in establishing input-to-state stability results, in the context of perturbed differential inclusions/switched systems, using locally Lipschitz candidate Lyapunov functions. These developments are then used in analyzing the stability problem for interconnections of differential inclusion, with an application in designing an observer-based controller for state-dependent switched systems
APA, Harvard, Vancouver, ISO, and other styles
5

England, Scott Alan. "Quantifying Dynamic Stability of Musculoskeletal Systems using Lyapunov Exponents." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/44784.

Full text
Abstract:
Increased attention has been paid in recent years to the means in which the body maintains stability and the subtleties of the neurocontroller. Variability of kinematic data has been used as a measure of stability but these analyses are not appropriate for quantifying stability of dynamic systems. Response of biological control systems depend on both temporal and spatial inputs, so means of quantifying stability should account for both. These studies utilized tools developed for the analysis of deterministic chaos to quantify local dynamic stability of musculoskeletal systems. The initial study aimed to answer the oft assumed conjecture that reduced gait speeds in people with neuromuscular impairments lead to improved stability. Healthy subjects walked on a motorized treadmill at an array of speeds ranging from slow to fast while kinematic joint angle data were recorded. Significant (p < 0.001) trends showed that stability monotonically decreased with increasing walking speeds. A second study was performed to investigate dynamic stability of the trunk. Healthy subjects went through a variety of motions exhibiting either symmetric flexion in the sagittal plane or asymmetric flexion including twisting at both low and high cycle frequencies. Faster cycle frequencies led to significantly (p<0.001) greater instability than slower frequencies. Motions that were hybrids of flexion and rotation were significantly (p<0.001) more stable than motions of pure rotation or flexion. Finding means of increasing dynamic stability may provide great understanding of the neurocontroller as well as decrease instances of injury related to repetitive tasks. Future studies should look in greater detail at the relationships between dynamic instability and injury and between local dynamic stability and global dynamic stability.
Master of Science
APA, Harvard, Vancouver, ISO, and other styles
6

Best, Eric A. "Stability assessment of nonlinear systems using the lyapunov exponent." Ohio University / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1175019061.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Tanaka, Martin L. "Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26580.

Full text
Abstract:
Low back pain is a common medical problem around the world afflicting 80% of the population some time in their life. Low back injury can result from a loss of torso stability causing excessive strain in soft tissue. This investigation seeks to apply existing methods to new applications and to develop new methods to assess torso stability. First, the time series averaged finite time Lyapunov exponent is calculated from data obtained during seated stability experiments. The Lyapunov exponent is found to increase with increasing task difficulty. Second, a new metric for evaluating torso stability is introduced, the threshold of stability. This parameter is defined as the maximum task difficulty in which dynamic stability can be maintained for the test duration. The threshold of stability effectively differentiates torso stability at two levels of visual feedback. Third, the state space distribution of the finite time Lyapunov exponent (FTLE) field is evaluated for deterministic and stochastic systems. Two new methods are developed to generate the FTLE field from time series data. Using these methods, Lagrangian coherent structures (LCS) are found for an inverted pendulum, the Acrobot, and planar wobble chair models. The LCS are ridges in the FTLE field that separate two inherently different types of motion when applied to rigid-body dynamic systems. As a result, LCS can be used to identify the boundaries of the basin of stability. Finally, these new methods are used to find the basin of stability from time series data collected from torso stability experiments. The LCS and basins of stability provide a richer understanding into the system dynamics when compared to existing methods. By gaining a better understanding of torso stability, it is hoped this knowledge can be used to prevent low back injury and pain in the future. These new methods may also be useful in evaluating other biodynamic systems such as standing postural sway, knee stability, or hip stability as well as time series applications outside the area of biomechanics.
Ph. D.
APA, Harvard, Vancouver, ISO, and other styles
8

Schroll, Arno. "Der maximale Lyapunov Exponent." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21994.

Full text
Abstract:
Bewegungsstabilität wird durch die Fähigkeit des neuromuskulären Systems adäquat auf Störungen der Bewegung antworten zu können erreicht. Einschränkungen der Stabilität werden z. B. mit Sturzrisiko in Verbindung gebracht, was schwere Konsequenzen für die Lebensqualität und Kosten im Gesundheitssystem hat. Nach wie vor wird debattiert, wie eine geeignete Bewertung von Stabilität vorgenommen werden kann. Diese Arbeit behandelt den maximalen Lyapunov Exponenten. Er drückt aus, wie sensitiv das System auf kleine Störungen eines Zustands reagiert. Eine Zeitreihe wird zunächst mittels zeitversetzter Kopien in einen mehrdimensionalen Raum eingebettet. In dieser rekonstruierten Dynamik berechnet man dann die Steigung der mittleren logarithmischen Divergenz initial naher Punkte. Die methodischen Konsequenzen für die Anwendung dieser Systemtheorie auf Bewegungen sind jedoch bislang unzureichend beleuchtet. Der experimentelle Teil zeigt klare Indizien, dass es bei Bewegungen weniger um die Analyse eines komplexen Systemdeterminismus geht, sondern um verschieden hohe dynamische Rauschlevel. Je höher das Rauschlevel, desto instabiler das System. Anwendung von Rauschreduktion führt zu kleineren Effektstärken. Das hat Folgen: Die Funktionswerte der Average Mutual Information, die bisher nur zur Bestimmung des Zeitversatzes genutzt wurden, können bereits Unterschiede in der Stabilität zeigen. Die Abschätzung der Dimension für die Einbettung (unabhängig vom verwendeten Algorithmus), ist stark von der Länge der Zeitreihe abhängig und wird bisher eher überschätzt. Die größten Effekte sind in Dimension drei zu beobachten und ein sehr früher Bereich zur Auswertung der Divergenzkurve ist zu empfehlen. Damit wird eine effiziente und standardisierte Analyse vorgeschlagen, die zudem besser imstande ist, Unterschiede verschiedener Bedingungen oder Gruppen aufzuzeigen.
Reductions of movement stability due to impairments of the motor system to respond adequately to perturbations are associated with e. g. the risk of fall. This has consequences for quality of life and costs in health care. However, there is still an debate on how to measure stability. This thesis examines the maximum Lyapunov exponent, which became popular in sports science the last two decades. The exponent quantifies how sensitive a system is reacting to small perturbations. A measured data series and its time delayed copies are embedded in a moredimensional space and the exponent is calculated with respect to this reconstructed dynamic as average slope of the logarithmic divergence curve of initially nearby points. Hence, it provides a measure on how fast two at times near trajectories of cyclic movements depart. The literature yet shows a lack of knowledge about the consequences of applying this system theory to sports science tasks. The experimental part shows strong evidence that, in the evaluation of movements, the exponent is less about a complex determinism than simply the level of dynamic noise present in time series. The higher the level of noise, the lower the stability of the system. Applying noise reduction therefore leads to reduced effect sizes. This has consequences: the values of average mutual information, which are until now only used for calculating the delay for the embedding, can already show differences in stability. Furthermore, it could be shown that the estimation of the embedding dimension d (independently of algorithm), is dependent on the length of the data series and values of d are currently overestimated. The greatest effect sizes were observed in dimension three and it can be recommended to use the very first beginning of the divergence curve for the linear fit. These findings pioneer a more efficient and standardized approach of stability analysis and can improve the ability of showing differences between conditions or groups.
APA, Harvard, Vancouver, ISO, and other styles
9

Thomas, Neil B. "The analysis and control of nonlinear systems using Lyapunov stability theory." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-08292008-063459/.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

McDonald, Dale Brian. "Feedback control algorithms through Lyapunov optimizing control and trajectory following optimization." Online access for everyone, 2006. http://www.dissertations.wsu.edu/Dissertations/Spring2006/D%5FMcDonald%5F050206.pdf.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Lyapunov stability"

1

Izobov, N. A. Lyapunov exponents and stability. Cambridge, UK: CSP/Cambridge Scientific Publishers, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Martyni︠u︡k, A. A. Stability of motions: The role of multicomponent Liapunov's functions. Cambridge, UK: Cambridge Scientific Pub, 2007.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

1943-, Abdulin R. Z., ed. Vector Lyapunov functions in stability theory. [Atlanta]: World Federation Publishers, 1996.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Martyni͡uk, A. A. Stability by Liapunov's matrix function method with applications. New York: Marcel Dekker, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Li︠a︡punov, A. M. Izbrannye trudy: Raboty po teorii ustoĭchivosti. Moskva: Nauka, 2007.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Shaĭkhet, L. E. Lyapunov functionals and stability of stochastic difference equations. London: Springer, 2011.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Gajić, Zoran. Lyapunov matrix equation in system stability and control. San Diego: Academic Press, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Javed, Qureshi Muhammad Tahir, ed. Lyapunov matrix equation in system stability and control. Mineola, N.Y: Dover Publications, 2008.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Gajić, Z. Lyapunov matrix equation in system stability and control. San Diego: Academic, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Difference Equations. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Lyapunov stability"

1

Johansson, Mikael. "Lyapunov Stability." In Piecewise Linear Control Systems, 41–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36801-9_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Sun, Xiaojuan. "Lyapunov Stability." In Encyclopedia of Systems Biology, 1144–45. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_532.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Westphal, L. C. "Lyapunov stability testing." In Sourcebook of Control Systems Engineering, 395–406. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1805-1_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Westphal, Louis C. "Lyapunov stability testing." In Handbook of Control Systems Engineering, 365–76. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1533-3_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Sastry, Shankar. "Lyapunov Stability Theory." In Interdisciplinary Applied Mathematics, 182–234. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3108-8_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Kong, Qingkai. "Lyapunov Stability Theory." In Universitext, 61–100. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11239-8_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Nguyen, Nhan T. "Lyapunov Stability Theory." In Model-Reference Adaptive Control, 47–81. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-56393-0_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Leipholz, Horst. "The Direct Method of Lyapunov." In Stability Theory, 77–88. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-663-10648-7_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Sontag, Eduardo D., and Héctor J. Sussmann. "General Classes of Control-Lyapunov Functions." In Stability Theory, 87–96. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9208-7_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Lavretsky, Eugene, and Kevin A. Wise. "Lyapunov Stability of Motion." In Robust and Adaptive Control, 225–61. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4396-3_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Lyapunov stability"

1

Tamer, Aykut, and Pierangelo Masarati. "Do We Really Need To Study Rotorcraft as Linear Periodic Systems?" In Vertical Flight Society 71st Annual Forum & Technology Display, 1–10. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10165.

Full text
Abstract:
This work discusses the application of Lyapunov Characteristic Exponents as a means of generalizing rotorcraft stability analysis. Stability estimation of linear time invariant and linear time periodic systems relies on eigenanalysis of special state transition matrices and implies simplifications on the nonlinear non-autonomous equations that govern rotorcraft stability. Lyapunov Characteristic Exponents provide quantitative information on the stability of nonlinear non-autonomous dynamical systems. Stability estimation using Lyapunov Characteristic Exponents does not require a special reference solution and agrees with the eigensolution of linear time invariant and Floquet-Lyapunov analysis of linear time periodic systems. Thus, they represent a natural generalization of conventional stability analysis. The Discrete QR method is used to practically estimate the Lyapunov Characteristic Exponents. The method is applied to rotorcraft related problems. Results are correlated with usual methods for linear time invariant and time periodic problems when possible.
APA, Harvard, Vancouver, ISO, and other styles
2

Allwright, J. C. "Orthogonal Lyapunov transformations and stability." In UKACC International Conference on Control (CONTROL '98). IEE, 1998. http://dx.doi.org/10.1049/cp:19980439.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Gao, Jianli, Balarko Chaudhuri, and Alessandro Astolfi. "Lyapunov-based Transient Stability Analysis." In 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022. http://dx.doi.org/10.1109/cdc51059.2022.9992811.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Galarza, Jose, Dumitru I. Caruntu, Simon Vasquez, and Robert Freeman. "Gait Stability Using Lyapunov Exponents." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-73242.

Full text
Abstract:
Abstract This work deals with the stability of the dynamics of human gait. This is a common exercise. The focus of this investigation is to analyze the knee angle time series and calculate the divergence for over-ground and treadmill walking. Experiments using motion capture technology are used to capture the movement. MATLAB software package is used to calculate the Lyapunov Exponents from the time series. Results are compared with similar studies in the literature. This work provides an insight on the level of stability for treadmill walking. A comparison with stability of normal gait might give an insight on how the treadmill can facilitate rehabilitation using gait.
APA, Harvard, Vancouver, ISO, and other styles
5

Rajaram, Rajeev, and Umesh Vaidya. "Robust stability analysis using Lyapunov density." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426681.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Zamani, Majid, and Rupak Majumdar. "A Lyapunov approach in incremental stability." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6160735.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Schrodel, Frank, Hong Liu, Ramy Elghandour, and Dirk Abel. "Lyapunov-based stability region computation approach." In 2015 European Control Conference (ECC). IEEE, 2015. http://dx.doi.org/10.1109/ecc.2015.7330995.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Somaraju, Ram, and Ian R. Petersen. "Lyapunov stability for Quantum Markov Processes." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160264.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Amato, F., R. Ambrosino, and M. Ariola. "Robust stability via polyhedral Lyapunov functions." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160329.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Bachelier, O., D. Arzelier, and D. Peaucelle. "Parameter-dependent Lyapunov d-stability bound." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7075936.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Lyapunov stability"

1

Scheinker, Alexander. Introduction to Control Theory. Part 3. State Space, Stability, and Lyapunov Functions. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1214625.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Nikoukhah, Ramine, Bernard C. Levy, and Alan S. Willsky. Stability, Stochastic Stationarity and Generalized Lyapunov Equations for Two-Point Boundary-Value Descriptor Systems,. Fort Belvoir, VA: Defense Technical Information Center, March 1988. http://dx.doi.org/10.21236/ada195645.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Event-Triggered Adaptive Robust Control for Lateral Stability of Steer-by-Wire Vehicles with Abrupt Nonlinear Faults. SAE International, July 2022. http://dx.doi.org/10.4271/2022-01-5056.

Full text
Abstract:
Because autonomous vehicles (AVs) equipped with active front steering have the features of time varying, uncertainties, high rate of fault, and high burden on the in-vehicle networks, this article studies the adaptive robust control problem for improving lateral stability in steer-by-wire (SBW) vehicles in the presence of abrupt nonlinear faults. First, an upper-level robust H∞ controller is designed to obtain the desired front-wheel steering angle for driving both the yaw rate and the sideslip angle to reach their correct values. Takagi-Sugeno (T-S) fuzzy modeling method, which has shown the extraordinary ability in coping with the issue of nonlinear, is applied to deal with the challenge of the changing longitudinal velocity. The output of the upper controller can be calculated by a parallel distributed compensation (PDC) scheme. Then an event-triggered adaptive fault-tolerant lower controller (ET-AFTC) is proposed to drive the whole SBW system driving the desired steering angle offered by the upper controller with fewer communication resources and strong robustness. By employing a backstepping technique, the tracking performance is improved. The dynamic surface control (DSC) approach is used to avoid the problem of repeated differentiations, and Nussbaum function is adopted to overcome the difficulty of unknown nonlinear control gain. Both the stability of the upper and lower controllers can be guaranteed by Lyapunov functions. Finally, the simulations of Matlab/Simulink are given to show that the proposed control strategy is effectively able to deal with the abrupt nonlinear fault via less communication resources and perform better in ensuring the yaw stability of the vehicle.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Lyapunov stability' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography