Relevant bibliographies by topics / Lyapunov stability theory

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

Academic literature on the topic 'Lyapunov stability theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 January 2023

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Journal articles on the topic "Lyapunov stability theory"

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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.

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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.
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Lamperski, Andrew, and Aaron D. Ames. "Lyapunov Theory for Zeno Stability." IEEE Transactions on Automatic Control 58, no. 1 (January 2013): 100–112. http://dx.doi.org/10.1109/tac.2012.2208292.

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Barreira, Luis, and Claudia Valls. "Stability theory and Lyapunov regularity." Journal of Differential Equations 232, no. 2 (January 2007): 675–701. http://dx.doi.org/10.1016/j.jde.2006.09.021.

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Shevitz, D., and B. Paden. "Lyapunov stability theory of nonsmooth systems." IEEE Transactions on Automatic Control 39, no. 9 (1994): 1910–14. http://dx.doi.org/10.1109/9.317122.

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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.

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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.
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Zhao, Rongyong, Ping Jia, Yan Wang, Cuiling Li, Yunlong Ma, and Zhishu Zhang. "Acceleration-critical density time-delay model for crowd stability analysis based on Lyapunov theory." MATEC Web of Conferences 355 (2022): 03019. http://dx.doi.org/10.1051/matecconf/202235503019.

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Crowd stability analysis is one of research hotspots to alleviate the severe situation of stampede accidents worldwide. Different from the conventional analysis models for crowd stability based on pedestrian density, this study analyses the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory. The critical range of crowd acceleration in crowd evacuation is obtained, a crowd merging acceleration-critical density time delay model is established, and a stability criterion of acceleration vector based on Lyapunov is obtained based on Lyapunov stability analysis. This provides new information for ensuring the stability of crowd movement in public places, assessing the stability of the crowd in the area, and taking reasonable protection and guidance measures prior to instability of a crowd flow.
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Moulay, E. "Morse theory and Lyapunov stability on manifolds." Journal of Mathematical Sciences 177, no. 3 (August 13, 2011): 419–25. http://dx.doi.org/10.1007/s10958-011-0468-6.

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Lakshmikantham, V., and N. S. Papageorgiou. "Cone-valued Lyapunov functions and stability theory." Nonlinear Analysis: Theory, Methods & Applications 22, no. 3 (February 1994): 381–90. http://dx.doi.org/10.1016/0362-546x(94)90028-0.

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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.

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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.
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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.

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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.
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Dissertations / Theses on the topic "Lyapunov stability theory"

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

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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/.

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Ahmadi, Amir Ali. "Non-monotonic Lyapunov functions for stability of nonlinear and switched systems : theory and computation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44206.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 87-90).
Lyapunov's direct method, which is based on the existence of a scalar function of the state that decreases monotonically along trajectories, still serves as the primary tool for establishing stability of nonlinear systems. Since the main challenge in stability analysis based on Lyapunov theory is always to nd a suitable Lyapunov function, weakening the requirements of the Lyapunov function is of great interest. In this thesis, we relax the monotonicity requirement of Lyapunov's theorem to enlarge the class of functions that can provide certicates of stability. Both the discrete time case and the continuous time case are covered. Throughout the thesis, special attention is given to techniques from convex optimization that allow for computationally tractable ways of searching for Lyapunov functions. Our theoretical contributions are therefore amenable to convex programming formulations. In the discrete time case, we propose two new sucient conditions for global asymptotic stability that allow the Lyapunov functions to increase locally, but guarantee an average decrease every few steps. Our first condition is nonconvex, but allows an intuitive interpretation. The second condition, which includes the first one as a special case, is convex and can be cast as a semidenite program. We show that when non-monotonic Lyapunov functions exist, one can construct a more complicated function that decreases monotonically. We demonstrate the strength of our methodology over standard Lyapunov theory through examples from three different classes of dynamical systems. First, we consider polynomial dynamics where we utilize techniques from sum-of-squares programming. Second, analysis of piecewise ane systems is performed. Here, connections to the method of piecewise quadratic Lyapunov functions are made.
(cont.) Finally, we examine systems with arbitrary switching between a finite set of matrices. It will be shown that tighter bounds on the joint spectral radius can be obtained using our technique. In continuous time, we present conditions invoking higher derivatives of Lyapunov functions that allow the Lyapunov function to increase but bound the rate at which the increase can happen. Here, we build on previous work by Butz that provides a nonconvex sucient condition for asymptotic stability using the first three derivatives of Lyapunov functions. We give a convex condition for asymptotic stability that includes the condition by Butz as a special case. Once again, we draw the connection to standard Lyapunov functions. An example of a polynomial vector field is given to show the potential advantages of using higher order derivatives over standard Lyapunov theory. We also discuss a theorem by Yorke that imposes minor conditions on the first and second derivatives to reject existence of periodic orbits, limit cycles, or chaotic attractors. We give some simple convex conditions that imply the requirement by Yorke and we compare them with those given in another earlier work. Before presenting our main contributions, we review some aspects of convex programming with more emphasis on semidenite programming. We explain in detail how the method of sum of squares decomposition can be used to efficiently search for polynomial Lyapunov functions.
by Amir Ali Ahmadi.
S.M.
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Shifman, Jeffrey Joseph. "The control of flexible robots." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385838.

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Herzog, David Paul. "Geometry's Fundamental Role in the Stability of Stochastic Differential Equations." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145150.

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We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. The result is proven by using Lyapunov functions and geometric control theory.
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Dierks, Travis. "Formation control of mobile robots and unmanned aerial vehicles." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2009. http://scholarsmine.mst.edu/thesis/pdf/Dierks_09007dcc806d7f16.pdf.

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Thesis (Ph. D.)--Missouri University of Science and Technology, 2009.
Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed January 13, 2009) Includes bibliographical references.
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Li, Yunyan. "Global finite-time observers for a class of nonlinear systems." Thesis, University of Pretoria, 2013. http://hdl.handle.net/2263/40825.

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The contributions of this thesis lie in the area of global finite-time observer design for a class of nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two different kinds of nonlinear global finite-time observers are designed by employing of finite-time theory and homogeneity properties with different methods. The global finite-time stability of both proposed observers is derived on the basis of Lyapunov theory. For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities, the first global finite-time observers are designed, where the global finite-time stability of the observation systems is achieved from two parts by combining asymptotic stability and local finitetime stability. The proposed observers can only be designed for the class of nonlinear systems with dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding with the two homogeneous items. One is homogeneous of degree greater than 1, which makes the observation error systems converging into a spherical area around the origin, and the other is of degree less than 1, which ensures local finite-time stability. The second global finite-time observers are also proposed based on the high-gain technique, which does not place any limitation on the dimension of the nonlinear systems. Compared with the first global finite-time observers, the newly designed observers have only one homogeneous term and a new gain update law where two new terms are introduced to dominate some terms in the nonlinearities and ensure global finite-time stability as well. The global finite-time stability is obtained directly based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in the proof. The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to the origin in finite-time. The parameters, initial conditions as well as the high gain do have some impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain is, the shorter the time it needs to converge. In order to show the performance of the two kinds of observers more clearly, two examples are provided and some comparisons are made between them. Through these, it can be seen that under the same parameters and initial conditions, although the amplitude of the observation error curve is slightly greater, the global finite-time observers with a new gain update law can make the observation error systems converge much more quickly than the global finite-time observers with two homogeneous terms. In the simulation results, one can see that, as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve their robustness and adaptiveness will be quite interesting, useful and challenging.
Thesis (PhD)--University of Pretoria, 2013.
gm2014
Electrical, Electronic and Computer Engineering
unrestricted
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Hui, Qing. "Nonlinear dynamical systems and control for large-scale, hybrid, and network systems." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24635.

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Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Haddad, Wassim; Committee Member: Feron, Eric; Committee Member: JVR, Prasad; Committee Member: Taylor, David; Committee Member: Tsiotras, Panagiotis
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Sousa, Júnior Celso de. "Análise de estabilidade de Lyapunov de algoritmos adaptativos com contribuições ao estudo do critério de módulo constante." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260851.

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Orientadores: João Marcos Travassos Romano, Romis Ribeiro de Faissol Attux
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: O problema de equalização adaptativa se vincula à busca por soluções iterativas que permitam reduzir ou eliminar os efeitos nocivos do canal de comunicação sobre um sinal transmitido de interesse. Uma vez que os sistemas adaptativos se baseiam em algoritmos capazes de ajustar os parâmetros de um filtro, pode-se considerar o conjunto equalizador / algoritmo adaptativo como um sistema dinâmico, o que termina por relacionar a possibilidade de obter uma solução satisfatória à noção de convergência. A análise de convergência de algoritmos de equalização adaptativa se desenvolveu, tipicamente, considerando algumas hipóteses para viabilizar o tratamento matemático, mas nem sempre tais hipóteses são estritamente válidas. Um exemplo clássico nesse sentido é o uso da teoria da independência. Neste trabalho, buscamos uma abordagem distinta do estudo das condições de estabilidade de algoritmos de equalização clássica baseada na teoria de Lyapunov. Essa teoria é geralmente utilizada no estudo de sistemas não-lineares, e apresenta um amplo histórico de resultados sólidos na área de controle adaptativo. Isso motiva o uso no campo de processamento de sinais. A primeira contribuição deste trabalho consiste em determinar, por meio da teoria de Lyapunov, a faixa de valores de passo de adaptação que garantem estabilidade do sistema de equalização para algoritmos baseados no critério deWiener e para o algoritmo do módulo constante. A partir dos resultados para estabilidade, investigar-se-á também a região de convergência para os pesos do algoritmo LMS, o que trará uma produtiva relação com a idéia de misadjustment. Como segunda linha de contribuição, será apresentada uma análise de um limitante inferior para o custo atingível e uma proposta de inicialização capaz de aumentar a probabilidade de convergência para o melhor ótimo gerado pelo critério para o algoritmo do módulo constante. Essa estratégia se baseia numa formulação do critério não-supervisionado de filtragem linear em termos da aplicação do critério de Wiener a uma estrutura polinomial. Os resultados obtidos revelam que a idéia é capaz de levar a um desempenho melhor que os do clássico método center spike e de uma estratégia de inicialização aleatória
Abstract: The problem of adaptive equalization is related to the search for iterative solutions that allow the reduction or the elimination of the noxious effects of a communication channel on a transmitted signal of interest. Since adaptive systems are based on algorithms capable of adjusting the parameters of a filter, the combination between equalizer and learning algorithm can be considered to form a dynamical system, which relates the possibility of obtaining a satisfactory solution to the convergence issue. The analysis of the convergence of adaptive equalization algorithms was developed, typically, considering certain simplifying hypotheses that, however, are not always strictly valid. A classical example that illustrates this assertion is the use of the so-called independence theory. In this work, it has been investigated a distinct approach to the study of stability conditions of classical methods based on Lyapunov theory. This theory is generally employed in the study of nonlinear systems, and presents a significant framework of sound results in the field of adaptive control, which motivates its use in the context of signal processing. The first contribution of this work consists of determining, by means of Lyapunov theory, the range of step-size values that ensure stability of the equalization system for algorithms based on the Wiener criterion and for the constant modulus algorithm. Using the obtained stability results, the convergence region for the parameters estimated via LMS is also investigated, which establishes an interesting connection with the notion of misadjustment. In a second line of study, we present an analysis of the lower bound for the attainable CM cost and an initialization heuristic capable of increasing the probability of convergence to the best optimum engendered by the constant modulus criterion. This strategy is based on a formulation of the unsupervised linear filtering criterion in terms of the application of the Wiener criterion to a polynomial structure. The obtained results reveal that the proposal is able to effectively lead to a performance level that is better than that achieved using the classical center spike method and a random approach
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
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Tognetti, Tais Calliero. "Controle de sistemas dinamicos : estabilidade absoluta, saturação e bilinearidade." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261053.

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Orientador: Pedro Luis Dias Peres
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Esta tese apresenta contribuições para a solução de problemas de análise de estabilidade e síntese de controladores por realimentação de estados de sistemas dinâmicos que possuem elementos não-lineares, por meio de condições na forma de desigualdades matriciais lineares e funções de Lyapunov. Para sistemas chaveados sujeitos a saturação nos atuadores, são fornecidas condições convexas para o cálculo de ganhos chaveados e robustos. A saturação é modelada como uma não-linearidade de setor e uma estimativa do domínio de estabilidade é determinada. Para sistemas lineares com incertezas politópicas e não-linearidades pertencentes a setores, são fornecidas condições convexas de dimensão finita para construir funções de Lur'e com dependência polinomial homogênea nos parâmetros. Se satisfeitas, as condições garantem a estabilidade para todo o domínio de incertezas e para todas as não-linearidades pertencentes ao setor e permitem o cômputo de controladores estabilizantes robustos por realimentação linear e não-linear. Para sistemas bilineares instáveis, contínuos e discretos no tempo, é proposto um procedimento para calcular um ganho estabilizante de controle por realimentação de estados. O método baseia-se na solução alternada de dois problemas de otimização convexa descritos por desigualdades matriciais lineares, fornecendo uma estimativa do domínio de estabilidade. Extensões para tratar controladores robustos e lineares variantes com parâmetros são também apresentadas.
Abstract: This thesis presents contributions to the solution of the problems of stability analysis and synthesis of state feedback controllers for dynamic systems with non-linear elements, by means of conditions based on linear matrix inequalities and Lyapunov functions. For switched systems subject to saturation in the actuators, convex conditions to design switched and robust controllers are presented. The saturation is modeled as a sector non-linearity and an estimate of the domain of stability is determined. For linear systems with polytopic uncertainties and sector non-linearities, convex conditions of finite dimension to build Lur'e functions with homogeneous polynomially parameter dependence are provided. If satisfied, the conditions guarantee the stability of the entire domain of uncertainty for all sector non-linearities, allowing the design of linear and non-linear robust state feedback stabilizing controllers. For continuous and discrete-time unstable bilinear systems, a procedure to design a state feedback stabilizing control gain is proposed. The method is based on the alternate solution of two convex optimization problems described by linear matrix inequalities, providing an estimate of the domain of stability. Extensions to handle robust and linear parameter varying controllers are also presented.
Doutorado
Automação
Doutor em Engenharia Elétrica
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Books on the topic "Lyapunov stability theory"

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1967-, Rosier Lionel, ed. Liapunov functions and stability in control theory. 2nd ed. Berlin: Springer, 2005.

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

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

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

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Zubov, Vladimir Ivanovich. Mathematical theory of the motion stability. Saint Petersburg: ["Mobilʹnostʹ pli︠u︡s"], 1997.

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Goebel, Rafal. Hybrid dynamical systems: Modeling, stability, and robustness. Princeton, N.J: Princeton University Press, 2012.

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Lakshmikantham, V. Practical stability of nonlinear systems. Singapore: World Scientific, 1990.

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Frédéric, Mazenc, and SpringerLink (Online service), eds. Constructions of Strict Lyapunov Functions. London: Springer London, 2009.

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A, Martynyuk Yu, ed. Uncertain dynamical systems: Stability and motion control. Boca Raton: Taylor & Francis, 2012.

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M, Matrosov V., and Sivasundaram S, eds. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems. Dordrecht: Springer Netherlands, 1991.

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Book chapters on the topic "Lyapunov stability theory"

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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.

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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.

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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.

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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.

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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.

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Boichenko, Vladimir A., Gennadij A. Leonov, and Volker Reitmann. "Attractors, stability and Lyapunov functions." In Dimension Theory for Ordinary Differential Equations, 79–173. Wiesbaden: Vieweg+Teubner Verlag, 2005. http://dx.doi.org/10.1007/978-3-322-80055-8_2.

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Barreira, Luis, and Yakov Pesin. "Lyapunov stability theory of differential equations." In Lyapunov Exponents and Smooth Ergodic Theory, 5–34. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/ulect/023/02.

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Hapaev, M. M. "Generalization of Lyapunov Second Method and Averaging in Stability Theory." In Averaging in Stability Theory, 19–101. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2644-1_2.

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Leine, Remco I., and Nathan van de Wouw. "Lyapunov Stability Theory for Measure Differential Inclusions." In Stability and Convergence of Mechanical Systems with Unilateral Constraints, 109–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-76975-0_6.

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Naboko, S. N., and C. Tretter. "Lyapunov stability of a perturbed multiplication operator." In Contributions to Operator Theory in Spaces with an Indefinite Metric, 309–26. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8812-7_17.

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Conference papers on the topic "Lyapunov stability theory"

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Rehman, Osama Abdur, and Naeem Iqbal. "Power system stability enhancement using Lyapunov theory." In 2016 International Conference on Emerging Technologies (ICET). IEEE, 2016. http://dx.doi.org/10.1109/icet.2016.7813255.

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Lyashevskiy, S., and Yaobin Chen. "The Lyapunov stability theory in system identification." In Proceedings of 16th American CONTROL Conference. IEEE, 1997. http://dx.doi.org/10.1109/acc.1997.611873.

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Tang, Minan, Jie Cao, Xiaoxiao Yang, Xiaoming Wang, and Baohui Gu. "Model reference adaptive control based on Lyapunov stability theory." In 2014 26th Chinese Control And Decision Conference (CCDC). IEEE, 2014. http://dx.doi.org/10.1109/ccdc.2014.6852467.

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Min-an, Tang, Wang Xiao-Ming, Cao Jie, and Cao Li. "On Lyapunov Stability Theory for Model Reference Adaptive Control." In 2017 4th International Conference on Information Science and Control Engineering (ICISCE). IEEE, 2017. http://dx.doi.org/10.1109/icisce.2017.221.

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Menguc, Engin Cemal, and Nurettin Acir. "Lyapunov stability theory based complex valued adaptive filter design." In 2014 22nd Signal Processing and Communications Applications Conference (SIU). IEEE, 2014. http://dx.doi.org/10.1109/siu.2014.6830210.

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Duchaine, Vincent, and Clement M. Gosselin. "Investigation of human-robot interaction stability using Lyapunov theory." In 2008 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2008. http://dx.doi.org/10.1109/robot.2008.4543531.

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Ryoo, Chang-Kyung, Yoon-Hwan Kim, and Min-Jea Tahk. "Capturability Analysis of PN Laws Using Lyapunov Stability Theory." In AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-4883.

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Menguc, E. C., and N. Acir. "Lyapunov Stability Theory Based Adaptive Filter Algorithm for Noisy Measurements." In 2013 UKSim 15th International Conference on Computer Modelling and Simulation (UKSim 2013). IEEE, 2013. http://dx.doi.org/10.1109/uksim.2013.50.

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Haddad, Wassim M., and Andrea L'Afflitto. "Finite-time partial stability theory and fractional Lyapunov differential inequalities." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7172175.

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Zhang, Shengguo, Shuo Zhang, Guoheng Zhang, and Wanchun Liu. "Parameter Optimization of Linear Control System Based on Lyapunov Stability Theory." In 2015 3rd International Conference on Mechatronics and Industrial Informatics. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/icmii-15.2015.27.

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Reports on the topic "Lyapunov stability theory"

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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.

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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.

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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.
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