Stability of Discrete-Time Systems with Time-Varying Delay: Delay Decomposition Approach

This article deals with the problem of obtaining delay-dependent stability conditions for a class of discrete-time systems with interval time-varying delay. Using the decomposition the delay interval into two unequal subintervals by tuning parameter a, a new interval delay-dependent Lyapunov-Krasovskii functional is constructed to derive novel delay-dependent stability conditions which are expressed in terms of linear matrix inequalities. This leads to reduction of conservatism in terms of the upper bounds of the maximum time-delay. The numerical examples show that the obtained result is less conservative than some existing ones in the literature.