New stability conditions for semilinear diffusion systems with time-delays

Oren Solomon, Emilia Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In the present paper, sufficient conditions for the exponential stability of nonlinear diffusion systems with infinite distributed and discrete time-varying delays are derived. Such systems arise in many applications, e.g. in population dynamics. The existing Lyapunov-based results on the stability of diffusion nonlinear systems treat either systems with infinite delays or the ones with discrete slowly varying delays (with the delay derivatives smaller than 1), where the conditions are delay-independent in the discrete delays. We introduce the Lyapunov-based analysis of systems with fast varying (without any constraints on the delay-derivative) discrete and infinite distributed delays. We derive delay-independent with respect to discrete delays stability criterion via a novel combination of Lyapunov-Krasovskii functionals and of the Halanay inequality in terms of Linear Matrix Inequalities (LMIs). Numerical examples illustrate the efficiency of the method.

Original languageEnglish
Title of host publication53rd IEEE Conference on Decision and Control,CDC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781479977468
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: 15 Dec 201417 Dec 2014

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/TerritoryUnited States
CityLos Angeles


  • Diffusion systems
  • Halanay inequality
  • Lyapunov-Krasovskii method
  • infinite delays
  • time-delays


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