Results 161 to 170 of about 695 (203)

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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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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Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks

SIAM Journal on Control and Optimization, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haitao Li 0001, Yuzhen Wang
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Higher Derivatives of Lyapunov Functions

Differential Equations, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Lyapunov function proof of Poincare's theorem

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002
One of the most fundamental results in analysing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincare's theorem. The proof of this result involves system analytic arguments along with the Hartman-Grobman theorem.
Wassim M. Haddad 0001, Sergey G. Nersesov, VijaySekhar Chellaboina   +2 more
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Semidefinite lyapunov functions stability and stabilization

Mathematics of Control, Signals, and Systems, 1996
The 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, Kalitine, Boris, Outbib, Rachid   +2 more
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