Strong practical stability and stabilization of uncertain 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. Previously reported work has defined the concept of strong practical stability for such cases and produced Linear Matrix Inequality (LMI) based necessary and sufficient conditions for it to hold. These can then be used as a basis for the design of a stabilizing control law. In this paper the (more practically relevant) case when there is uncertainty associated with the process description which is assumed to be of the norm bounded form is considered.