Lyapunov stability of a class of hybrid dynamic systems
type: Item
instance of: scholarly article
title: Lyapunov stability of a class of hybrid dynamic systems
zbMATH Open document ID: 0952.93102
DOI: 10.1016/S0005-1098(99)00144-2
published in: Automatica
publication date: 2001-01-11T00:00:00Z
review text: The authors consider the ``hybrid system'' \[ \dot x= g(x,m(\tau)) \] with \(m(\tau)\) the ``discrete state'' of the system and \(x\) the continuous state. When the trajectory meets the set \(\{x(\tau): (x(\tau), m(\tau))= 0\}\) some switching will occur \[ x(\tau_k^+)= h(x(\tau_k^-), m(\tau_k^-)), \qquad m(\tau_k^+)= \psi(x(\tau_k^-), m(\tau_k^-)). \] Stability of the invariant sets of such systems is considered using a kind of Lyapunov function interpreted as an abstract measure of systems potential energy.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C30
zbMATH DE Number: 1394983
zbMATH Keywords: hybrid system
zbMATH Keywords: stability of the invariant sets
zbMATH Keywords: Lyapunov function
author: Zhengguo Li
author: Cheong Boon Soh
author: Xinhe Xu
MaRDI profile type: Publication
cites work: Periodicity and chaos from switched flow systems: contrasting examples of discretely controlled continuous systems
cites work: Nonlinear systems
cites work: Q4284052
cites work: Lyapunov stability theory of nonsmooth systems
Wikidata QID: Q127088178
full work available at URL: s0005-1098(99)00144-2
OpenAlex ID: W2076749838
description: scientific article; zbMATH DE number 1394983