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

Shanaz Tiwari, Yuan Wang, Zhong-Ping Jiang

Research output: Contribution to journalArticle

Abstract

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
Volume19
Issue number1
StatePublished - 2012

Fingerprint

Small Gain Theorem
Time-delay Systems
Large-scale Systems
Time delay
Disturbance
Functional Differential Equations
Stability Analysis
Subsystem
Large scale systems
Output
Differential equations
Theorem
Strategy

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Analysis
  • Discrete Mathematics and Combinatorics

Cite this

Nonlinear small-gain theorems for large-scale time-delay systems. / Tiwari, Shanaz; Wang, Yuan; Jiang, Zhong-Ping.

In: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, Vol. 19, No. 1, 2012, p. 27-63.

Research output: Contribution to journalArticle

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