Exponential stability of a state-dependent delay system

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

In this paper we study exponential stability of the trivial solution of the state-dependent delay system ẋ(t) = ∑i=1m A i(t)x(t - τi(t, xt)). We show that under mild assumptions, the trivial solution of the state-dependent system is exponentially stable if and only if the trivial solution of the corresponding linear time-dependent delay system ẏ(t) = ∑i=1m Ai(t)y(t - τi(t, 0)) is exponentially stable. We also compare the order of the exponential stability of the nonlinear equation to that of its linearized equation. We show that in some cases, the two orders are equal. As an application of our main result, we formulate a necessary and sufficient condition for the exponential stability of the trivial solution of a threshold-type delay system.

Original languageEnglish
Pages (from-to)773-791
Number of pages19
JournalDiscrete and Continuous Dynamical Systems
Volume18
Issue number4
Publication statusPublished - Aug 2007

Fingerprint

State-dependent Delay
Delay Systems
Exponential Stability
Asymptotic stability
Trivial
Type Systems
Nonlinear equations
Linear Time
Nonlinear Equations
If and only if
Necessary Conditions
Dependent
Sufficient Conditions

Keywords

  • Exponential stability
  • Order of exponential stability
  • State-dependent delay
  • Threshold delay

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Exponential stability of a state-dependent delay system. / Győri, I.; Hartung, F.

In: Discrete and Continuous Dynamical Systems, Vol. 18, No. 4, 08.2007, p. 773-791.

Research output: Contribution to journalArticle

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