Accession Number:

ADA458859

Title:

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

Descriptive Note:

Technical paper

Corporate Author:

CALIFORNIA UNIV SANTA BARBARA DEPT OF MECHANICAL AND ENVIRONMENTAL ENGINEERING

Personal Author(s):

Report Date:

2005-01-01

Pagination or Media Count:

8.0

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 belongs 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. We then show that the SDGC remains satisfied under the addition of the spatially periodic operator, if this operator is small 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 the system is exponentially stable. The results are demonstrated through simple illustrative examples.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE