TY - GEN

T1 - On stability and the spectrum determined growth condition for spatially periodic systems

AU - Fardad, Makan

AU - Bamieh, Bassam

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:39649092243

SN - 1424401712

SN - 9781424401710

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3956

EP - 3961

BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

T2 - 45th IEEE Conference on Decision and Control 2006, CDC

Y2 - 13 December 2006 through 15 December 2006

ER -