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. † Department of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto 606, JAPAN. e-mail: [email protected] FAX: +81-75-761-2437 ‡ Department of Control Engineering, Faculty of Engineering, Tokyo Institute of Technology,Oh-Okayama 152, JAPAN. e-mail: [email protected] FAX: +81-3-3729-1774 For all correspondence, contact the first author. Suggested running head: Internal and External Stability for Infinite-Dimensional Systems