Equivalence of Input-Output Stability and Exponential Stability for Infinite Dimensional Systems

摘要

For a wide class of infinite dimensional linear systems it is shown that if the state space realization is exponentially stabilizable and detectable, then exponential stability is equivalent to input-output stability of the transfer function. The equivalence conditions are readily checked for spectral and delay systems. While one would expect that systems with a well defined nuclear Hankel operator would be included in the above class, it is not proved. Output feedback control may result in a weaker form of exponential stability, but this is a consequence of the well posedness question in state space and seems unavoidable.