Guaranteed Cost Control of State-Delay System Based on the Equivalent-Input-Disturbance Approach

Abstract

This paper considers a guaranteed cost control problem for state-delay systems with exogenous disturbances for a proper plant. The equivalent-input-disturbance (EID) approach is extended to be able to handle a state-delay system. A new control law is constructed that incorporates an EID estimate in order to ensure a satisfactory control performance. A stability condition for the closed-loop system is provided in terms of a linear matrix inequality, using the Lyapunov function method. Furthermore, a guaranteed cost control state feedback control law and a state observer are designed, based on the linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the validity of the method.