PROOF 1861-5252/ c  2009 TSSD Transactions on Systems, Signals & Devices Vol. 4, No. 1, pp.1-139 Stabilization Through Output Feedback Control for Uncertain Switched Discrete Time Systems E. Maherzi, 1 M. Besbes, 1 J. Bernussou, 2 and R. Mhiri 1,3 1 R´ eseaux et Machines Electriques (RME) Institut Sup´ erieur des Sciences Appliqu´ ees et de Technologie, centre urbain Tunis-nord, B.P. 676, 1080 Tunis, Tunisia. 2 Laboratoire d’Analyse et d’Architecture des Syst` emes (LAAS) 7 Avenue du Colonel Roch-31077 Toulouse Cedex 4, France. 3 Facult´ e des Sciences de Tunis Campus Universitaire B.P. 1060, Tunis, Tunisia. Abstract This paper discusses the robust stabilization of discrete switched systems, focusing on the design of a robust static output feed- back control and dynamic output control based on a switched observer. The results are derived using the direct Lyapunov approach and the polyquadratic function concept. The stabi- lization conditions are written through linear matrix inequalities relations. The polyquadratic Lyapunov approach provides a con- structive way to tackle uncertainty in the switched framework. The feasibility is illustrated on an example of discrete uncertain switched discrete time system. Keywords: Robust control, stability and stabilization, switched discrete time systems, output feedback control and observer control. 1. Introduction The literature has shown a growing interest on switched systems since switched control systems exist widely in engineering technology and so- cial systems [7, 8, 20]. Switched systems are an important class of hybrid systems defined by a set whose elements are dynamic continuous (or dis- crete) time models and a commutation law which governs, in time, the jumps between the elements, defining a non stationary dynamic system. Many important progress and remarkable achievements have been made