Stability Analysis of Discrete-Time System with Time-Varying Delay Based on Generalized Reciprocally Convex Matrix Inequality

Abstract

This paper concerns the stability analysis of discrete-time systems(DTS) with a time-varying delay(TVD). Firstly, by adding double summation terms, an appropraite Lyapunov-Krasovskii functional (LKF) is constructed. Then, the generalized reciprocally convex matrix inequality(GRCMI), together with the Jensen-based summation inequality(JBI) and the Wirtinger-based summation inequality(WBI), is used to estimate the forward difference of the LKF. Finally, a new delay-dependent stability criterion is established. The stability criterion show lower conservatism and require lower computational burden than results previously proposed, whose advantages are demonstrated via a numerical instance.