NDLI: On Stability and the Spectrum Determined Growth Condition for Spatially Periodic Systems

Content Provider	IEEE Xplore Digital Library
Author	Fardad, M. Bamieh, B.
Copyright Year	2006
Description	Author affiliation: Dept. of Mech. & Environ. Eng., California Univ., Santa Barbara, CA (Fardad, M.; Bamieh, B.)
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 $e^{At}$ 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
Starting Page	3956
Ending Page	3961
File Size	227928
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377216
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability Control systems USA Councils Distributed parameter systems Linear systems Spatial resolution
Content Type	Text
Resource Type	Article

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