On Exponential Stability of Systems with Point, Distributed and Volterra-type Delayed Dynamics

The global uniform exponential stability independent of delay (g.u.e.s.i.d.) is investigated for a wide class of time-delay systems that may involve both point and distributed delays on finite intervals as well as infinitely distributed Volterra integro-differential dynamics. The stability problem i...

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Bibliographic Details
Published inApplicable analysis Vol. 82; no. 9; pp. 875 - 882
Main Authors De La Sen, M., Luo, Ningsu
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.09.2003
Subjects
Ams Subject Classifications: 93d20
Dynamic Systems
Functional Equations
Time-delay Systems
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Summary:The global uniform exponential stability independent of delay (g.u.e.s.i.d.) is investigated for a wide class of time-delay systems that may involve both point and distributed delays on finite intervals as well as infinitely distributed Volterra integro-differential dynamics. The stability problem is considered as a robust stability one with respect to an auxiliary system which may be defined very freely. The proposed method allows a very important generalisation related to the usual problem statement in the literature when the auxiliary system is defined by deleting the whole delayed dynamics. Conditions are established that ensure that the Laplace operator characterising the system has a bounded inverse on the closed complex right-half plane. The analysis is slightly modified for investigating uniform stability dependent of delay.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036810310001596647