A Lyapunov-based small-gain theorem for interconnected switched systems

Guosong Yang, Daniel Liberzon

Research output: Contribution to journalArticlepeer-review


Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input-to-state stable (non-ISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic stability (GAS) of the interconnected system. For each switched system, with the constraints on the switching signal being modeled by an auxiliary timer, a correspondent hybrid system is defined to enable the construction of a hybrid ISS Lyapunov function. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected system is globally asymptotically stable.

Original languageEnglish (US)
Pages (from-to)47-54
Number of pages8
JournalSystems and Control Letters
StatePublished - Apr 2015


  • Hybrid systems
  • Interconnected systems
  • Lyapunov methods
  • Small-gain theorems
  • Switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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