Stabilizing randomly switched systems

Debasish Chatterjee, Daniel Liberzon

Research output: Contribution to journalArticlepeer-review


This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable.These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results, together with universal formulae for feedback stabilization of nonlinear systems, constitute our primary tools for control design.

Original languageEnglish (US)
Pages (from-to)2008-2031
Number of pages24
JournalSIAM Journal on Control and Optimization
Issue number5
StatePublished - 2011


  • Feedback stabilization
  • Randomly switched systems
  • Semi-Markov switching signals
  • Stochastic stability

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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