State Feedback Controller Design for Discrete-Time Linear System with Time-Varying Delay Using a New Lyapunov-Krasovskii Functional

This paper presents the stabilization problem of linear discrete-time systems with time-varying delay using a new Lyapunov-Krasovskii (LK) functional. A tighter estimate of the forward difference of LK functional is obtained by invoking the summation inequality and reciprocally convex combination lemma. A delay-dependent condition for the existence of state-feedback controller is derived in linear matrix inequality (LMI) framework which ensures asymptotic stability in the sense of Lyapunov. The effectiveness of the proposed results is demonstrated through numerical examples.