Strong practical stability and stabilization of uncertain discrete linear repetitive processes

Abstract

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass, respectively, where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak, and stability along the pass is too strong for meaningful progress to be made. This, in turn, has led to the concept of strong practical stability for such cases, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality based tests, which then extend to allow robust control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that also extend to allow control law design. © 2011 John Wiley & Sons, Ltd.