EQUIVALENCE OF INTERNAL AND EXTERNAL 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 infinity 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 infinity condition. Examples are given to illustrate the theory.