Systems with gamma-distributed delays: A Lyapunov-based analysis

Oren Solomon, Emilia Fridman

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

Abstract

In the present paper, sufficient conditions for the exponential stability of linear systems with gamma-distributed delays are presented. Such systems arise in populations dynamics, in traffic flow models, in networked control systems and in other engineering problems. Our main challenge is the stability conditions, where the delay is stabilizing, i.e. the corresponding system with the zero-delay is not asymptotically stable. The results are derived by using augmented Lyapunov functionals, were we generalize the earlier results of [1] and [9], regarding distributed delays and finite constant kernels, to the infinite delay case by extending the corresponding Jensen's integral inequalities and Lyapunov-Krasovskii constructions. Poly topic uncertainties in the system matrices can be easily included in the analysis. Numerical examples illustrate the efficiency of the method. Thus, for the traffic flow model on the ring, where the delay is stabilizing, the resulting stability region almost coincides with the theoretical one found in [11] via the frequency domain analysis.

Original languageEnglish
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages318-323
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 10 Dec 201313 Dec 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference52nd IEEE Conference on Decision and Control, CDC 2013
Country/TerritoryItaly
CityFlorence
Period10/12/1313/12/13

Keywords

  • Consensus
  • Gamma-distributed delay
  • Lyapunov-Krasovskii method
  • Stabilization by delay

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