Stability analysis and stabilization of randomly switched systems

Debasish Chatterjee, Daniel Liberzon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals are considered: the first is a jump stochastic process that satisfies a statistically slow switching condition; the second and the third are jump stochastic processes with independent identically distributed values at jump times together with exponential and uniform holding times, respectively. For each of the three cases we first establish sufficient conditions for stochastic stability of the switched system when the subsystems do not possess control inputs; not every subsystem is required to be stable in the latter two cases. Thereafter we design feedback controllers when the subsystems are affine in control and are not all zeroinput stable, with the control space being general subsets of ℝm. Our analysis results and universal formulae for feedback stabilization of nonlinear systems for the corresponding control spaces constitute the primary tools for control design.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2643-2648
Number of pages6
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - Jan 1 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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