Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations

Liangjian Hu, Xuerong Mao, Liguo Zhang

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

One of the important issues in the study of hybrid stochastic differential delay equations (SDDEs) is the automatic control, with consequent emphasis being placed on the asymptotic analysis of stability and boundedness. In the study of asymptotic properties, the robust stability has received a great deal of attention. The theory of robust stability shows how much perturbation a given stable hybrid SDDE can tolerate so that its perturbed system remains stable. Almost all results so far on the robust stability require that the underlying SDDEs be either linear or nonlinear with linear growth condition. However, little is known on the robust stability of nonlinear hybrid SDDEs without the linear growth condition, which is one of the key topics in this paper. The other key topic is the robust boundedness. The aim here is to answer the question: how much perturbation can a given asymptotically bounded hybrid SDDE tolerate so that its perturbed system remains asymptotically bounded?
Original languageEnglish
Pages (from-to)2319
Number of pages2332
JournalIEEE Transactions on Automatic Control
Volume58
Issue number9
Early online date29 Mar 2013
DOIs
Publication statusPublished - 1 Sep 2013

Keywords

  • Brownian motion
  • Markovian switching
  • generalized Ito's formula
  • stochastic differential delay equations
  • exponential stability
  • asymptotic boundedness

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