Stochastic stability of singularly perturbed nonlinear systems

Cheng Tang, Tamer Başar

Research output: Contribution to journalArticlepeer-review


The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the “total stability" type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for the full-order system as long as the singular perturbation parameter is sufficiently small and a stochastic small gain condition is satisfied. The result is general in that it holds for a broad class of disturbances, and resembles similar results for deterministic systems.

Original languageEnglish (US)
Pages (from-to)399-404
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2001


  • Input-to-state stability
  • Singular perturbations
  • Stochastic systems

ASJC Scopus subject areas

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


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