Equivalence of internal and extremal stability for a class of distributed systems
type: Item
instance of: scholarly article
title: Equivalence of internal and extremal stability for a class of distributed systems
zbMATH Open document ID: 0732.93057
DOI: 10.1007/BF02570569
author: Yutaka Yamamoto
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1991-01-01T00:00:00Z
review text: It is well known that for infinite-dimensional systems, exponential stability is not necessarily determined by the location of spectrum. Similarly, transfer functions in the \(H^{\infty}\) space need not possess an exponentially stable realization. This paper addresses this problem for a class of impulse responses called pseudorational. In this class, it is shown that the difficulty is related to classical complex analysis, especially that of entire functions of exponential type. The infinite-product representation for such entire functions makes it possible to prove that stability is indeed determined by the location of spectrum or by a modified \(H^{\infty}\) condition. Examples are given to illustrate the theory.
reviewed by: He Chungyou
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 4211927
zbMATH Keywords: external stability
zbMATH Keywords: exponential stability
zbMATH Keywords: Examples
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02570569
OpenAlex ID: W1986880064
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description: scientific article; zbMATH DE number 4211927