Reciprocal Convex Approach to Delay-dependent Stability of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, we consider the problem of delay-dependent stability of a class of uncertain linear discrete-time systems with time-varying delay using Lyapunov functional approach. By exploiting a candidate Lyapunov functional, and using reciprocal convex approach in the delay-dependent stability analysis, a less conservative robust stability criterion is derived in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed criterion over a recently reported result is validated using a standard numerical example.