Delay feedback control in exponential stabilization of linear time-varying systems with input delay

In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved Lyapunov–Krasovskii functional, new sufficient conditions for the exponential stabilization of the system are derived to design memory feedback controller which makes the system exponentially stabilizable. The conditions are given in terms of the solution of appropriate Riccati differential equations, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. An application to robust control of uncertain linear control systems with input delay as well as illustrative examples to show the effectiveness of the obtained results is given.