Stability analysis of discrete-time switched systems with time-varying delays via a new summation inequality

This paper proposes a new summation inequality, which improves the conservatism in the stability analysis for discrete-time systems with time-varying delay. In order to show the effectiveness of the proposed inequality, which provides general lower bound of the summation quadratic term of the form ∑s=abxT(s)Mx(s), a delay-dependent stability criterion for such systems is derived within the framework of linear matrix inequalities (LMIs). Going one step forward, the proposed inequality is applied to a stability problem in discrete-time switched systems with time-varying delays. The advantages of employing the proposed summation inequality are illustrated via three numerical examples.