Results 211 to 220 of about 43,098 (261)
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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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Dynamics and Control, 1995
This is an interesting paper in the spirit of the Russian school in stability theory which considers the problem of finding an ``optimal'' Lyapunov function for a linear autonomous differential equation. Various optimality criteria are formulated and finding the corresponding Lyapunov functions is reduced to optimization problems: a two-person game or ...
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This is an interesting paper in the spirit of the Russian school in stability theory which considers the problem of finding an ``optimal'' Lyapunov function for a linear autonomous differential equation. Various optimality criteria are formulated and finding the corresponding Lyapunov functions is reduced to optimization problems: a two-person game or ...
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Rendiconti del Circolo Matematico di Palermo, 2004
The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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Higher derivatives of Lyapunov functions and cone-valued Lyapunov functions
Nonlinear Analysis: Theory, Methods & Applications, 1996The authors are interested in the stability properties of the trivial solution of the system \(x'=f(t,x)\) and wish to use the higher derivatives of a single Lyapunov function to investigate them. If the resulting comparison system satisfies the required quasimonotone property, one can use a variant of the method of vector Lyapunov functions.
Köksal, S., Lakshmikantham, V.
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Journal of Dynamic Systems, Measurement, and Control, 1989
The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a
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The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a
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Robust stability via polyhedral Lyapunov functions
2009 American Control Conference, 2009In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be “universal” for the uncertain system under consideration if the search of a Lyapunov function that ...
Amato, F., Ambrosino, R., Ariola, M.
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Semidefinite lyapunov functions stability and stabilization
Mathematics of Control, Signals, and Systems, 1996The paper gives some weakening of the basic Lyapunov theorems by obtaining stability and asymptotic stability for nonnegatively definite Lyapunov functions. These results allow simpler proofs for some previously known results and some extension of the stabilization results for systems that are affine in the control.
Iggidr, Abderrahman +2 more
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2020
The present chapter is centered around the CLF paradigm that underlies the principal feedback design methods such as Bellman dynamic programming in optimal control and nonlinear \(\mathscr {H}_\infty \) approach in the robust synthesis. CLFs are first illustrated with quadratic forms, which result in a simple LMI criterion of the asymptotic stability ...
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The present chapter is centered around the CLF paradigm that underlies the principal feedback design methods such as Bellman dynamic programming in optimal control and nonlinear \(\mathscr {H}_\infty \) approach in the robust synthesis. CLFs are first illustrated with quadratic forms, which result in a simple LMI criterion of the asymptotic stability ...
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Higher Derivatives of Lyapunov Functions
Differential Equations, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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