INTERNAL AND EXTERNAL STABILITY AND ROBUST STABILITY CONDITION FOR A CLASS OF INFINITE-DIMENSIONAL SYSTEMS

In the current study of robust stability of infinite-dimensional systems, internal exponential stability is not necessarily guaranteed. This paper introduces a new class of impulse responses called R, in which the usual notion of L2-input/output stability guarantees not only external but also internal exponential stability. The result is applied to derive a closed-loop stability condition, and a version of the small gain theorem with internal exponential stability; this leads to a robust stability condition that also assures internal stability. An application to repetitive control systems is shown to illustrate the results.