Robust observer-based H∞ stabilization of switched discrete-time linear systems with parameter uncertainties

This paper presents a robust observer-based $H_\infty$ controller design method via LMIs for a class of switched discrete-time linear systems with $l_2$-bounded disturbances and parameter uncertainties. The main contribution of this paper consists in a new and judicious use of the slack variables coming from Finsler's lemma. We show analytically how the proposed slack variables allow to eliminate some bilinear matrix coupling. The validity and effectiveness of the proposed design methodology are shown through two numerical examples.