H_∞ observer-based stabilization of switched discrete-time linear systems

This paper deals with observer-based H∞ controller design method via LMIs for a class of switched discretetime linear systems with l2-bounded disturbances. The main contribution of this note consists in a new and judicious use of the slack variables coming from Finsler’s lemma. We clarify analytically how the proposed slack variables allows to eliminate some bilinear matrix coupling. The validity and effectiveness of the proposed design methodology are shown through a numerical example.