Strong practical stability and H∞ disturbance attenuation for discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The original stability theory for these processes 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. Previously reported work has introduced strong practical stability as an alternative for such cases and produced Linear Matrix Inequality (LMI) based necessary and sufficient conditions for this property to hold, together with algorithms for stabilizing control law design. This paper considers the problem of strong practical stability with guaranteed levels of performance, where a solution is developed for strong practical stability with a prescribed disturbance attenuation performance as measured by the H
_∞
norm.