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

This paper is devoted to the study of observer-based ℋ
_∞
controller design method via LMIs for a class of switched discrete-time linear systems with ℓ
₂
-bounded disturbances. The main contribution of this work 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 illustrated through a numerical example.