Equivalence of internal and extremal stability for a class of distributed systems
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.
scientific article; zbMATH DE number 4211927