Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

This paper presents robust stability and stabilisation problems of linear discrete-time systems with interval time-varying state-delay. By invoking a new Lyapunov-Krasovskii functional, a less conservative delay-dependent robust stability criterion is derived in terms of linear matrix inequalities (LMIs) using the summation inequality in combination with the extended reciprocally convex inequality. Then, a delay-dependent stabilisation problem of discrete-time systems is explored by designing a state feedback controller. The superiority of the proposed result over existing ones is demonstrated through numerical examples.