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Constructions of Strict Lyapunov Functions

open access: yes, 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
core   +5 more sources

On almost Lyapunov functions

53rd 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.
Daniel Liberzon   +2 more
openaire   +1 more source

On quadratic lyapunov functions

IEEE Transactions on Automatic Control, 2003
A topological structure, as a subset of [0,2/spl pi/)/sup L//spl times//spl Ropf//sub +//sup n-1/, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral ...
Daizhan Cheng   +2 more
openaire   +1 more source

Control Minkowski–Lyapunov functions

Automatica, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Optimization of lyapunov functionals

Meccanica, 1975
The 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.
openaire   +2 more sources

Lyapunov functionals and matrices

Annual Reviews in Control, 2010
Abstract In this contribution we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear time delay systems. Some lower and upper bounds for the functionals are given. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices.
openaire   +1 more source

Robust Minkowski–Lyapunov functions

Automatica, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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