Contraction analysis for a class of nondifferentiable systems with applications to stability and network synchronization
2014 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 52, no 5, 3203-3227 p.Article in journal (Refereed) Published
In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched nondifferentiable systems satisfying Caratheodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems.
Place, publisher, year, edition, pages
2014. Vol. 52, no 5, 3203-3227 p.
contraction theory, convergence, piecewise smooth systems, networks
Control Engineering Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-157581DOI: 10.1137/120883001ISI: 000344748000021ScopusID: 2-s2.0-84911091329OAI: oai:DiVA.org:kth-157581DiVA: diva2:771219
QC 201412122014-12-122014-12-112014-12-12Bibliographically approved