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Stability and Stabilization for uncertain switched systems, a polyquadratic Lyapunov approach

This paper discusses the problem of stability and stabilization of discrete time switched systems, focusing on the design of a robust state feedback control, and a robust static output feedback control. The results are derived using the direct Lyapunov approach and the poly-quadratic function concept. The stabilization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a constructive way to tackle uncertainty in the switched framework. The feasibility is illustrated on two examples of discrete time uncertain switched systems.