Global behavior in nonlinear systems with delayed feedback

Anatoli F. Ivanov, Manuel A. Pinto, Sergei I. Trofimchuk

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The problem of global stability in scalar delay differential equations of the form ẋ(t) = f(x(t - τ)) - g(x(t)) is studied. Functions f and g are continuous and such that the equation assumes a unique equilibrium. Two types of the sufficient conditions for the global asymptotic stability of the unique equilibrium are established: (i) delay independent, and (ii) conditions involving the size τ of the delay. Delay independent stability conditions make use of the global stability in the limiting (as τ → ∞) difference equation g(xn+1) = f(xn): the latter always implying the global stability in the differential equation for all values of the delay τ ≥ 0. The delay dependent conditions involve the global attractivity in specially constructed one-dimensional maps (difference equations) that include the nonlinearities f and g, and the delay τ.

Original languageEnglish (US)
Pages (from-to)4420-4421
Number of pages2
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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