On stability and the spectrum determined growth condition for spatially periodic systems

Makan Fardad, Bassam Bamieh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider distributed parameter systems where the underlying dynamics are spatially periodic on the real line. We examine the problem of exponential stability, namely whether the semigroup eAt decays exponentially in time. It is known that for distributed systems the condition that the spectrum of A belong to the open left-half plane is, in general, not sufficient for exponential stability. Those systems for which this condition is sufficient are said to satisfy the Spectrum Determined Growth Condition (SDGC). In this work we separate A into a spatially invariant operator and a spatially periodic operator. We find conditions for the spatially invariant part to satisfy the SDGC, and show that the SDGC remains satisfied under the addition of a spatially periodic operator if this operator is 'weak' enough relative to the spatially invariant one. A similar method is used to derive conditions which guarantee that A has left-half plane spectrum and thus establish exponential stability.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Pages3956-3961
Number of pages6
StatePublished - Dec 1 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

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

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

ASJC Scopus subject areas

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

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  • Cite this

    Fardad, M., & Bamieh, B. (2006). On stability and the spectrum determined growth condition for spatially periodic systems. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 3956-3961). [4177408] (Proceedings of the IEEE Conference on Decision and Control).