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Stability and Lyapunov Theory

In this chapter, we explore mathematical tools for assessing the stability, convergence, and boundedness of trajectories in generally nonlinear dynamical systems. We delve into the seminal theorems introduced by A.
Yiannis Karayiannidis
exaly   +4 more sources

Morse theory and Lyapunov stability on manifolds [PDF]

Journal of Mathematical Sciences, 2011
The aim of this article is to recall the main theorems of Morse theory and to infer some corollaries for the problem of Lyapunov stability on manifolds. It makes a link between Morse theory and the general theory of the Lyapunov stability for dynamical systems.
Moulay, Emmanuel, E. Moulay
exaly   +5 more sources

Lyapunov stability theory of nonsmooth systems [PDF]

IEEE Transactions on Automatic Control, 1994
Summary: This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle for a class of nonsmooth Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient are derived.
Daniel W. Shevitz, Brad Paden
exaly   +2 more sources

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Lyapunov stability theory

Lecture Notes in Control and Information Sciences, 2005
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Lyapunov Theory for Zeno Stability

IEEE Transactions on Automatic Control, 2013
Zeno 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
openaire   +2 more sources

Lyapunov Stability Theory for Nonlinear Nabla Fractional Order Systems

IEEE Transactions on Circuits and Systems II: Express Briefs, 2021
Lyapunov method is a powerful tool for studying the stability of dynamic systems while existing work mainly focuses on the asymptotic stability and rarely concerns the boundedness. Under this background, this brief aims to discuss the boundedness of nonlinear nabla fractional order systems.
Yiheng Wei
exaly   +3 more sources

Cone-valued Lyapunov functions and stability theory

Nonlinear Analysis: Theory, Methods & Applications, 1994
The authors consider a differential system of the form \(x'= f(t,x)\), \(x\in\mathbb{R}^ n\). They deal with stability in terms of two measures, a notion of stability which allows a unified treatment of a number of different definitions existing in the literature.
V Lakshmikantham
exaly   +2 more sources

Lyapunov's direct method in stability theory (review)

International Applied Mechanics, 1992
zbMATH 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), 1997
A 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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Lyapunov Stability Theory

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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