On stability of randomly switched nonlinear systems

Debasish Chatterjee, Daniel Liberzon

Research output: Contribution to journalArticlepeer-review


This note is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure stability and stability in the mean using Lyapunov-based methods when individual subsystems are stable and a certain "slow switching" condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous- timeMarkov chains; our results, therefore, hold forMarkovian jump systems in particular. For systems with control inputs, we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems.

Original languageEnglish (US)
Pages (from-to)2390-2394
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 2007


  • Almost sure and mean stochastic stability
  • Random switching
  • Stabilization
  • Switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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