On stability of linear retarded distributed parameter systems of parabolic type

Yury Orlov, Emilia Fridman

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


In this chapter the stability analysis via Lyapunov-Krasovskii method is extended to linear parabolic time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay derivative, which is less than 1. Sufficient delay-independent asymptotic stability conditions are derived. These conditions are given in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation with the Dirichlet boundary conditions, these LOIs are represented in terms of standard Linear Matrix Inequalities (LMIs).

Original languageEnglish
Title of host publicationTopics in Time Delay Systems
Subtitle of host publicationAnalysis, Algorithms and Contr
EditorsJean Jacques Loiseau, Wim Michiels, Silviu-Iulian Niculescu, Rifat Sipahi
Number of pages11
StatePublished - 2009

Publication series

NameLecture Notes in Control and Information Sciences
ISSN (Print)0170-8643


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