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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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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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Founded Lyapunov–Bogdanov Functionals
Differential Equations, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Borukhov, V. T., Kvetko, O. M.
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Control Minkowski–Lyapunov functions
Automatica, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lyapunov and Lyapunov-like functions
2007Lyapunov 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 ...
Franco Blanchini, Stefano Miani
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Optimization of lyapunov functionals
Meccanica, 1975The problem of optimality of Lyapunov Functionals is posed in terms of the requirements of a specific problem. The optimizationprocess is based on a method used to construct Lyapunov Functionals called “Path Integral Synthesis” proposed by the authors.
Golia, Carmine, Abel, Jacob M.
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Robust Minkowski–Lyapunov functions
Automatica, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weak Converse Lyapunov Theorems and Control-Lyapunov Functions
SIAM Journal on Control and Optimization, 2004Summary: Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set \({\mathcal A}\) for a differential inclusion that is defined on \(\mathbb{R}^n\), is locally Lipschitz on \(\mathbb{R}^n \backslash{\mathcal A}\), and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on
Kellett, Christopher M., Teel, Andrew R.
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Robust control Minkowski–Lyapunov functions
Automatica, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonuniform Dichotomies via Lyapunov Functions
Milan Journal of Mathematics, 2014The main aim of this paper is to study the relationship between the nonuniform exponential dichotomy and so-called strict Lyapunov functions for abstract nonautonomous linear equations. In other words, exponential dichotomies are characterized in terms of Lyapunov functions. Both direct and reverse theorems are presented.
Barreira, Luis, Valls, Claudia
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Lyapunov Functions and Cone Families
Journal of Statistical Physics, 2012We 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 ...
Barreira, Luis +2 more
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