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Relevant bibliographies by topics / Lyapunov time

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Academic literature on the topic 'Lyapunov time'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Lyapunov time"

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Zagrebina, I. S. "Lyapunov inequality for time scales." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 2 (April 2008): 47–48. http://dx.doi.org/10.20537/vm080216.

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Bohner, Martin, Stephen Clark, and Jerry Ridenhour. "Lyapunov inequalities for time scales." Journal of Inequalities and Applications 2002, no. 1 (2002): 829403. http://dx.doi.org/10.1155/s102558340200005x.

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Evans, Denis J. "Time correlation relation for Lyapunov exponents." Physical Review Letters 69, no. 3 (July 20, 1992): 395–97. http://dx.doi.org/10.1103/physrevlett.69.395.

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Kharitonov, V. L., and E. Plischke. "Lyapunov matrices for time-delay systems." Systems & Control Letters 55, no. 9 (September 2006): 697–706. http://dx.doi.org/10.1016/j.sysconle.2006.01.005.

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Tanaka, Toshiyuki, Kazuyuki Aihara, and Masao Taki. "Lyapunov exponents of random time series." Physical Review E 54, no. 2 (August 1, 1996): 2122–24. http://dx.doi.org/10.1103/physreve.54.2122.

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Pyragas, K. "Conditional Lyapunov exponents from time series." Physical Review E 56, no. 5 (November 1, 1997): 5183–88. http://dx.doi.org/10.1103/physreve.56.5183.

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Bryant, Paul, Reggie Brown, and Henry D. I. Abarbanel. "Lyapunov exponents from observed time series." Physical Review Letters 65, no. 13 (September 24, 1990): 1523–26. http://dx.doi.org/10.1103/physrevlett.65.1523.

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Balibrea, Francisco, and María Victoria Caballero. "Using Lyapunov exponents in time series." IEICE Proceeding Series 1 (March 17, 2014): 447–49. http://dx.doi.org/10.15248/proc.1.447.

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Li, Huijuan, and Qingxia Ma. "Finite-Time Lyapunov Functions and Impulsive Control Design." Complexity 2020 (October 27, 2020): 1–9. http://dx.doi.org/10.1155/2020/5179752.

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In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

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Gao, Wenhua, Feiqi Deng, Ruiqiu Zhang, and Wenhui Liu. "Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/809290.

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This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

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Dissertations / Theses on the topic "Lyapunov time"

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Manolescu, Crina Iulia. "Lyapunov transformations and control." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266339.

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Marikar, Mohamed Tariq. "Polyhedral Lyapunov functions and stabilization under polyhedral constraints." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266114.

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Leitenmaier, Lena. "Iterative methods and convergence for the time-delay Lyapunov equation." Thesis, KTH, Numerisk analys, NA, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-192633.

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The delay Lyapunov equation is a matrix boundary value problem arising in the characterization of many properties of time-delay systems, for example stability analysis. Its numerical treatment is challenging. For the special case of single-delay systems, a new algorithm based on a delay free formulation has recently been proposed. Using this formulation it is possible to obtain a linear system of equations with an equivalent solution. This linear system can be solved with GMRES or a similar iterative method, thus allowing to efficiently solve large-scale problems. In addition to the preconditioner proposed in the literature, on the basis of solving a T-Sylvester equation, a new preconditioner for this iterative method is derived here. It uses the diagonals of the time-delay system’s n × n state matrices to compute an approximation of the action of the n² × n² matrix associated to the linear system. Computational cost and convergence of this new preconditioner are investigated and proved. Examples for its efficiency under certain conditions are given and it is compared to the preconditioner from the literature. A pseudospectral analysis of the corresponding operators is conducted to get a better understanding of the convergence of both preconditioners. Several ways to obtain pseudospectra based convergence estimates are presented and their descriptiveness for different types of problems is discussed.
Lyapunovekvationen för tidsfördröjningssystem är ett matrisrandvärdesproblem och är viktigt för att karakterisera tidsfördröjningssystem, till exempel igenom stabilitetsanalys. Denna ekvation är svår att lösa numeriskt. För specialfallet med bara en fördröjningsterm har en ny algoritm baserad på en fördröjningsfri formulering föreslagits. Använder man denna formulering är det möjligt att få ett linjärt system av ekvationer med en ekvivalent lösning. Detta system kan lösas med en effektiv metod för storskaliga problem som GMRES eller någon liknande iterativ metod. Förutom den förkonditionerare some föreslagits in litteraturen, som är baserad på att lösa en T-Sylvester ekvation, härleds här en ny förkonditionerare. Den använder diagonalerna av tidsfördröjningssystemets n × n statusmatriser för att beräkna en uppskattning av verkningen av n² × n² matrisen associerad med det linjära systemet. Beräkningskostnader och konvergens av denna nya förkonditionerare undersöks och bevisas. Dessutom genomförs en analys som bygger på pseudospectra av båda förkonditionerares tillhöriga operatorerna för att få en bättre förståelse av deras konvergens. Flera sätt för att uppnå pseudospectrabaserad konvergensuppskattningar presenteras. En analys genomförs för att visa hur väl uppskattningarna beskriver konvergensen.

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Lopez, Ramirez Francisco. "Control and estimation in finite-time and in fixed-time via implicit Lyapunov functions." Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I063/document.

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Dans ce travail, on montre des nouveaux résultats pour l’analyse et la synthèse des systèmes stables en temps fini et fixe. Ce genre des systèmes convergent exactement à un point d’équilibre dans une quantité du temps qui est fini et, dans le cas de systèmes stables en temps fixe, dans un temps maximal constant qui ne dépend pas des conditions initiales du système.Les chapitres 2 et 3 portent sur des résultats d’analyse ; ce premier present des conditions nécessaires et suffisants pour la stabilité en temps fixe des systèmes autonomes continues tandis que ce dernier combine l’approche de la fonction implicite de Lyapunov avec des résultats de stabilisation ISS pour étudier la robustesse de ce genre de systèmes.Les chapitres 4 et 5 présentent des résultats pratiques liés á la procédure de synthèse des contrôleurs et des observateurs. Le chapitre 4 emploie la méthode de la fonction de Lyapunov implicite afin d’obtenir des observateurs convergents en temps fini et fixe pour les systèmes linéaires MIMO. Le chapitre 5 utilise des propriétés d’homogénéité et des fonctions de Lyapunov implicites pour synthétiser un contrôleur de sortie en temps fixe pour une chaîne d’intégrateurs. Les résultats obtenus ont été validés par des simulations numériques et le chapitre 4 contient des tests de performance sur un pendule rotatif
This work presents new results on analysis and synthesis of finite-time and fixed-time stable systems, a type of dynamical systems where exact convergence to an equilibrium point is guaranteed in a finite amount of time. In the case of fixed-time stable system, this is moreover achieved with an upper bound on the settling-time that does not depend on the system’s initial condition.Chapters 2 and 3 focus on theoretical contributions; the former presents necessary and sufficient conditions for fixed-time stability of continuous autonomous systems whereas the latter introduces a framework that gathers ISS Lyapunov functions, finite-time and fixed-time stability analysis and the implicit Lyapunov function approach in order to study and determine the robustness of this type of systems.Chapters 4 and 5 deal with more practical aspects, more precisely, the synthesis of finite-time and fixed-time controllers and observers. In Chapter 4, finite-time and fixed-time convergent observers are designed for linear MIMO systems using the implicit approach. In Chapter 5, homogeneity properties and the implicit approach are used to design a fixed-time output controller for the chain of integrators. The results obtained were verified by numerical simulations and Chapter 4 includes performance tests on a rotary pendulum

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

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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.

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

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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.

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Chao, Chien-Hsiang. "Robust stabilization of linear time-invariant uncertain systems via Lyapunov theory." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/53928.

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This dissertation is concerned with the problem of synthesizing a robust stabilizing feedback controller for linear time-invariant systems with constant uncertainties that are not required to satisfy matching conditions. Only the bounds on the uncertainties are required and no statistical property of the uncertainties is assumed. The systems under consideration are described by linear state equations with uncertainties. I.e. x(t) = A̅(γ)x(t) +B̅(γ)u(t), where A̅(γ) is an n x n matrix and B̅(γ) is an n x m matrix. Lyapunov theory is exploited to establish the conditions for stabilizability of the closed loop system. We consider a Lyapunov function with an uncertain symmetric positive definite matrix P. The uncertain matrix P satisfies the Lyapunov equation A^TP + PA + Q = 0, where the matrix A is in companion form and the matrix Q is symmetric and positive definite. In the solution of the Lyapunov equation, m rows of the matrix P are fixed in our approach of designing a robust controller. We derive necessary and sufficient conditions on these fixed m rows of the matrix P such that for given positive definite and symmetric Q the solution of the Lyapunov equation yields a positive definite matrix P and a companion matrix A that is Hurwitz. A discontinuous robust stabilizing controller is given. Linear controller design is also investigated in this research. Under the same assumptions for the existence of a stabilizing discontinuous controller, we show that a linear robust stabilizing controller always exists. The dissertation includes three examples to illustrate the design procedures for robust controllers. Example 2 shows that the design procedure may be applied to time-varying nonlinear systems.
Ph. D.

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Montagnier-Michau, Pierre Jean Andre. "Dynamics and control of time-periodic mechanical systems via floquet-lyapunov theory." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=38242.

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Many practical problems in engineering can be modelled as linear dynamical systems with periodically varying coefficients. This thesis proposes a new design method for the control of these linear time-periodic systems.
First, Floquet-Lyapunov theory is used to derive the Floquet factors of the state-transition matrix of a given system. We introduce a novel approach to obtain every real representation. It is demonstrated that the periodicity of the periodic factor can be determined a priori using a constant matrix, which we call the Yakubovich matrix, based upon the signs of the eigenvalues of the monodromy matrix. We then introduce a novel method for the numerical computation of the Floquet factors, relying upon a boundary-value problem formulation and the Yakubovich matrix.
In the second part, we use the invertibility of the controllability Gramian and a specific form for the feedback gain matrix to build a novel control law for the closed-loop system. The new controller can be full-state or observer-based and allows the control engineer to assign all the invariants of the system, i.e. the full monodromy matrix. Deriving the feedback matrix requires first solving a matrix integral equation for the periodic Floquet factor of the new state-transition matrix of the closed-loop system. This is achieved via a spectral method, which can then be further refined by a boundary-value problem formulation. Computational efficiency of the scheme may be further improved by performing the controller synthesis on the transformed system obtained from the reducibility theorem.
Finally, the effectiveness of the method is illustrated with an application to a quick-return mechanism using a software toolbox developed for MATLAB(TM).

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Zhang, Xiping. "Parameter-Dependent Lyapunov Functions and Stability Analysis of Linear Parameter-Dependent Dynamical Systems." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/5270.

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The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones. This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity. In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order can be reduced even further. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems. The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results. In the last part of the thesis, topics for future investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.

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Orstavik, Odd-Halvdan Sakse. "Analysis of chaotic multi-variate time-series from spatio-temporal dynamical systems." Thesis, University College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314071.

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Books on the topic "Lyapunov time"

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Kharitonov, Vladimir L. Time-Delay Systems: Lyapunov Functionals and Matrices. Boston: Birkhäuser Boston, 2013.

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1958-, Mielke Alexander, ed. Multi-pulse evolution and space-time chaos in dissipative systems. Providence, R.I: American Mathematical Society, 2009.

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Kharitonov, Vladimir. Time-Delay Systems: Lyapunov Functionals and Matrices. Birkhäuser, 2012.

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Kharitonov, Vladimir. Time-Delay Systems: Lyapunov Functionals and Matrices. Birkhäuser, 2012.

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Sanjuan, Miguel A. F., and Juan C. Vallejo. Predictability of Chaotic Dynamics: A Finite-time Lyapunov Exponents Approach. Springer, 2019.

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Sanjuan, Miguel A. F., and Juan C. Vallejo. Predictability of Chaotic Dynamics: A Finite-time Lyapunov Exponents Approach. Springer, 2018.

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Book chapters on the topic "Lyapunov time"

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Agarwal, Ravi, Donal O’Regan, and Samir Saker. "Lyapunov Inequalities." In Dynamic Inequalities On Time Scales, 175–214. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11002-8_4.

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Pesin, Yakov, Agnieszka Zelerowicz, and Yun Zhao. "Time Rescaling of Lyapunov Exponents." In Advances in Dynamics, Patterns, Cognition, 29–40. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53673-6_3.

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Zhang, Lixian, Ting Yang, Peng Shi, and Yanzheng Zhu. "Time-Varying Lyapunov Function Approach." In Analysis and Design of Markov Jump Systems with Complex Transition Probabilities, 207–24. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28847-5_10.

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Holzfuss, Joachim, and Ulrich Parlitz. "Lyapunov exponents from time series." In Lecture Notes in Mathematics, 263–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0086675.

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Artstein, Zvi. "The Lyapunov method (a tutorial)." In Hybrid and Real-Time Systems, 2. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0014708.

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Agarwal, Ravi P., Martin Bohner, and Abdullah Özbekler. "Lyapunov-Type Inequalities for Dynamic Equations on Time Scales." In Lyapunov Inequalities and Applications, 513–90. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69029-8_8.

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Sadlo, Filip. "Lyapunov Time for 2D Lagrangian Visualization." In Mathematics and Visualization, 167–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44900-4_10.

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Parlitz, Ulrich. "Estimating Lyapunov Exponents from Time Series." In Chaos Detection and Predictability, 1–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48410-4_1.

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Shaikhet, Leonid. "Difference Equations with Continuous Time." In Lyapunov Functionals and Stability of Stochastic Difference Equations, 227–81. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6_9.

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Ochoa, Gilberto, Juan E. Velázquez, Vladimir L. Kharitonov, and Sabine Mondié. "Lyapunov Matrices for Neutral Type Time Delay Systems." In Topics in Time Delay Systems, 61–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02897-7_6.

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Conference papers on the topic "Lyapunov time"

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Lazar, Mircea, and Rob Gielen. "On parameterized Lyapunov and control Lyapunov functions for discrete-time systems." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5716952.

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Debeljkovic, D. Lj, M. Aleksendric, N. Yi-Yong, and Q. L. Zhang. "Lyapunov and Non-Lyapunov Stabilty of Linear Discrete Time Delay Systems." In 4th International Conference on Control and Automation. Final Program and Book of Abstracts. IEEE, 2003. http://dx.doi.org/10.1109/icca.2003.1595032.

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Kaczorek, Tadeusz, and Przemyslaw Przyborowski. "Positive Continuous-Time Linear Lyapunov Systems." In EUROCON 2007 - The International Conference on "Computer as a Tool". IEEE, 2007. http://dx.doi.org/10.1109/eurcon.2007.4400242.

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Klose, Bjoern, and Gustaaf Jacobs. "Video: 3D finite-time Lyapunov exponent." In 71th Annual Meeting of the APS Division of Fluid Dynamics. American Physical Society, 2018. http://dx.doi.org/10.1103/aps.dfd.2018.gfm.v0086.

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Mattioni, Mattia, Salvatore Monaco, and Dorothee Normand-Cyrot S. "Lyapunov stabilization of discrete-time feedforward dynamics." In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. http://dx.doi.org/10.1109/cdc.2017.8264289.

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Jiang, Xia, Xianlin Zeng, Jian Sun, and Jie Chen. "Distributed Algorithm for Discrete-Time Lyapunov Equations." In 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV). IEEE, 2018. http://dx.doi.org/10.1109/icarcv.2018.8581279.

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Lopez-Ramirez, F., D. Efimov, A. Polyakov, and W. Perruquettil. "On Implicit Finite- Time and Fixed- Time ISS Lyapunov Functions." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619502.

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Colonius, Fritz, and Wolfgang Kliemann. "Stability of Time Varying Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0276.

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Abstract:

Abstract The stability behavior of time varying systems can be studied using the concept of Lyapunov exponents and their corresponding Lyapunov subspaces. For linear time varying systems the entire Lyapunov spectrum can be approximated by the Floquet exponents of periodic systems. This leads to a variety of stability results, including the characterization of stability radii. Furthermore, a structural stability type theorem shows that stability features of time varying hyperbolic systems persist under small perturbations. For nonlinear time varying systems a stable manifold theorem allows us to interpret the linear results for the nonlinear system locally around an equilibrium point.

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Miron, Philippe, Jérôme Vétel, and Andre Garon. "Efficient computation of the finite-time Lyapunov exponent." In 21st AIAA Computational Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-3086.

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Maggia, Marco, Kenneth D. Mease, and Benjamin F. Villac. "Finite-Time Lyapunov Analysis of Orbits Near L1." In AIAA/AAS Astrodynamics Specialist Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-4352.

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Reports on the topic "Lyapunov time"

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Mitra, Joydeep, Mohammed Ben-Idris, Omar Faruque, Scott Backhaus, and Sidart Deb. A Lyapunov Function Based Remedial Action Screening Tool Using Real-Time Data. Office of Scientific and Technical Information (OSTI), March 2016. http://dx.doi.org/10.2172/1421846.

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Branicki, Michal, and Stephen Wiggins. Finite-Time Lagrangian Transport Analysis: Stable and Unstable Manifolds of Hyperbolic Trajectories and Finite-Time Lyapunov Exponents. Fort Belvoir, VA: Defense Technical Information Center, August 2009. http://dx.doi.org/10.21236/ada513245.

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