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Dynamic Lyapunov functions

Automatica, 2011
Abstract Lyapunov functions are a fundamental tool to investigate the stability properties of equilibrium points in linear or nonlinear systems. Unfortunately, even if the existence of Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems, the actual computation of the analytic expression of the ...
Sassano M., Astolfi A.
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On almost Lyapunov functions [PDF]

open access: possible53rd IEEE Conference on Decision and Control, 2014
We study asymptotic stability properties of nonlinear systems in the presence of “almost Lyapunov” functions which decrease along solutions in a given region not everywhere but rather on the complement of a set of small volume. Nothing specific about the structure of this set is assumed besides an upper bound on its volume.
Charles Ying   +2 more
openaire   +1 more source

Lyapunov Functions and Cone Families [PDF]

open access: possibleJournal of Statistical Physics, 2012
We describe systematically the relation between Lyapunov functions and nonvanishing Lyapunov exponents, both for maps and flows. This includes a brief survey of the existing results in the area. In particular, we consider separately the cases of nonpositive and arbitrary Lyapunov functions, thus yielding optimal criteria for negativity and positivity ...
Claudia Valls   +2 more
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Lyapunov and Lyapunov-like functions

2007
Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary ...
Stefano Miani, Franco Blanchini
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Attractors and Lyapunov Functions

2020
The main tool in estimating dimensions of invariant sets and entropies of dynamical systems developed in this book is based on Lyapunov functions. In this chapter we introduce the basic concept of global attractors. The existence of a global attractor for a dynamical system follows from the dissipativity of the system.
Volker Reitmann, Nikolay Kuznetsov
openaire   +2 more sources

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