What is Polytopic Uncertainties

This chapter aims to study the problem of stability analysis, and robust exponential stabilization for a class of switched linear systems with polytopic uncertainties is reviewed. A sufficient condition based on the average dwell time that guarantees the exponential stability of uncertain switched linear systems is given. First, the iterative learning control is presented to build a formulation ensuring the exponential stability of the given system. The integrated design of this ILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. The results are obtained through original connection with the notion of stability along the pass for 2D repetitive systems. An overview of the stabilization methods of switched discrete systems found in the literature is outlined. All the given formulations are presented in terms of LMIs. A numerical simulation example is established, showing the effectiveness of the proposed method.