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A novel Lyapunov functional for stability of time-varying delay systems via matrix-refined-function

Automatica, 2017
This paper is concerned with the development of novel stability criteria for time-varying delayed systems. To this end, a new function which consisted of two quadratic functions with a special structural matrix is established to be a Lyapunov functional ...
Ju H Park, Tae H Lee
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On the Construction of Lyapunov Functions

SIAM Journal on Applied Mathematics, 1969
the same. These results are used to obtain new instability results for the Hill equation which extend the classical results of Lyapunov and Haupt. Finally, we show that a Lyapunov function for w' = 2Bw can be used to algorithmically obtain a Lyapunov function for y' = By along with certain verifiable conditions from which stability properties of y ...
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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 ...
Franco Blanchini, Stefano Miani
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Weak Converse Lyapunov Theorems and Control-Lyapunov Functions

SIAM Journal on Control and Optimization, 2004
Summary: 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
Christopher M. Kellett, Andrew R. Teel
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Founded Lyapunov–Bogdanov Functionals

Differential Equations, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Borukhov, V. T., Kvetko, O. M.
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Logical composition of Lyapunov functions

International Journal of Control, 2011
This article introduces the use of R-functions to compose single Lyapunov functions (LFs) via classic Boolean operators, with the aim to obtain a rich family of non-conventional, generally non-convex functions. The main benefit of the proposed composition is the nice geometric interpretation, since it corresponds to intersection and union operations in
Aldo Balestrino, Andrea Caiti, Emanuele Crisostomi   +2 more
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Higher derivatives of Lyapunov functions and cone-valued Lyapunov functions

Nonlinear Analysis: Theory, Methods & Applications, 1996
The 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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Lyapunov Functions and Cone Families

Journal 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 ...
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
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Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations

SIAM Journal on Applied Dynamical Systems, 2015
Given that a Lyapunov function is known for a particular system, we outline an approach for determining terms in the system that can be replaced by similar terms that include delay, without changing the global stability. The approach is based on adding integral terms to the original Lyapunov function so that the new Lyapunov derivative is still ...
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Constructions of Strict Lyapunov Functions

2009
The construction of strict Lyapunov functions is a challenging problem that is of significant ongoing research interest. Although converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, the Lyapunov functions that converse theory provides are often abstract and nonexplicit, and therefore may not lend ...
Malisoff, Michael, Mazenc, Frédéric
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