Nonlinear small-gain theorems for large-scale time-delay systems

Shanaz Tiwari, Yuan Wang, Zhong Ping Jiang

Research output: Contribution to journalArticlepeer-review


This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.

Original languageEnglish (US)
Pages (from-to)27-63
Number of pages37
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Issue number1
StatePublished - 2012


  • Input-to-output stability
  • Input-to-state stability
  • Nonlinear small-gain
  • Razumikhin theorems
  • Time-delay systems

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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