Strong practical stability and control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest. The stability theory for these processes currently consists 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 paper develops the concept of strong practical stability for such cases together with LMI based necessary and sufficient conditions. These are then used as a basis for control law design.