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Lyapunov Theory for Zeno Stability
IEEE Transactions on Automatic Control, 2013Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood.
Andrew G. Lamperski, Aaron D. Ames
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Lyapunov's direct method in stability theory (review)
International Applied Mechanics, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lakshmikantham, V., Martynyuk, A. A.
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The Lyapunov stability theory in system identification
Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997A new identification framework is developed for some long-standing problems. The convergence conditions of the process parameters: identification are explored from the Lyapunov stability theory, and this paper applies the second method toward a unified treatment of the convergence of the identification process.
S. Lyashevskiy, null Yaobin Chen
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1999
The study of the stability of dynamical systems has a very rich history. Many famous mathematicians, physicists, and astronomers worked on axiomatizing the concepts of stability. A problem, which attracted a great deal of early interest was the problem of stability of the solar system, generalized under the title “the N-body stability problem.” One of ...
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The study of the stability of dynamical systems has a very rich history. Many famous mathematicians, physicists, and astronomers worked on axiomatizing the concepts of stability. A problem, which attracted a great deal of early interest was the problem of stability of the solar system, generalized under the title “the N-body stability problem.” One of ...
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2014
Basic concepts for the Lyapunov stability are introduced. Conditions are obtained for the stability of linear equations with constant, periodic, and general variable coefficients. Linearization and Lyapunov functions are used to deal with nonlinear stability problems.
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Basic concepts for the Lyapunov stability are introduced. Conditions are obtained for the stability of linear equations with constant, periodic, and general variable coefficients. Linearization and Lyapunov functions are used to deal with nonlinear stability problems.
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A. M. Lyapunov's stability theory—100 years on
IMA Journal of Mathematical Control and Information, 1992Summary: On 12 October 1892 (according to the modern calendar) Alexandr Mikhailovich Lyapunov defended his doctoral thesis `The general problem of the stability of motion' at Moscow University. A brief history of Lyapunov's life and tragic death is given, and followed by a section highlighting the important ideas in his thesis of 1892.
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2018
Stability of nonlinear systems are discussed in this chapter. Lyapunov stability, asymptotic stability, and exponential stability of an equilibrium point of a nonlinear system are defined. The Lyapunov’s direct method is introduced as an indispensable tool for analyzing stability of nonlinear systems.
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Stability of nonlinear systems are discussed in this chapter. Lyapunov stability, asymptotic stability, and exponential stability of an equilibrium point of a nonlinear system are defined. The Lyapunov’s direct method is introduced as an indispensable tool for analyzing stability of nonlinear systems.
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Stability theory and Lyapunov's second method
Archive for Rational Mechanics and Analysis, 19631. Introduct ion In two papers appearing in t949 and t956, MASSERA [8, 9] made a number of significant advances in LYAPUNOV'S second method and the theory of stability of ordinary differential equations. He extended the work of LYAPUNOV [31, MALKIN [4--71 and others and arrived at both necessary and sufficient conditions for stability in terms of a ...
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