A formula for frequency responses of distributed systems with one spatial variable

Mihailo R. Jovanović, Bassam Bamieh

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We develop a method for the exact determination of frequency responses for a class of infinite dimensional systems. In particular, we consider distributed systems in which a spatial independent variable belongs to a finite interval, and in which the inputs and outputs are spatially distributed over the same interval. We show that an explicit formula for the Hilbert-Schmidt norm of the operator-valued frequency response can be obtained whenever the underlying operators are represented by a forced two point boundary value state-space realizations (TPBVSR). This formula involves finite dimensional computations with matrices whose dimension is at most four times larger than the order of the underlying differential operator. Two examples are provided to illustrate the procedure.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalSystems and Control Letters
Volume55
Issue number1
DOIs
StatePublished - Jan 1 2006

Keywords

  • Frequency responses
  • Infinite-dimensional systems
  • Two point boundary value state-space realizations

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