Stabilization of Perturbed Linear Systems with Time-Varying Delays in States and Inputs∗

The design of state feedback controllers and observers are proposed in this paper for a class of multi-input-multi-output linear systems with uncertainties and time varying delays both in states and control inputs. By using Lyapunov stability theorem, a sufficient condition is found for computing the state feedback gains of controllers and the gains of observers in order to regulate the closed-loop systems in spite of the existence of parameters variations as well as delays. This sufficient condition contains two inequalities, one of which is linear matrix inequality (LMI), which can be solved by utilizing the computer’s software package. The globally asymptotic stability of the closed-loop system is guaranteed if the solution which satisfies the proposed sufficient condition exists. An application is given for demonstrating the feasibility of the proposed control method, whose performance is also compared to an existing sliding mode control scheme.