Observer based stabilization of linear time delay systems using new augmented LKF

This paper addresses the stabilization problem of linear time-varying delay systems with unmeasurable states. A novel augmented Lyapunov–Krasovskii functional (LKF) is proposed that effectively accounts for the impact of time delays, and an observer based stabilization controller is developed employing linear matrix inequality (LMI) based optimization technique. The utilization of extended reciprocally convex matrix inequality (ERCMI) is employed in this work to establish less conservative stabilization conditions within the framework of linear matrix inequalities (LMIs). By formulating a convex optimization problem, the observer gain and controller gains are determined. Simulation results are used to validate the design, and two numerical examples are considered to prove the usefulness of the proposed method over existing methods.