A Robust Guaranteed Cost Sliding Mode Controller for a Class of Uncertain Time-delay Systems

This paper presents a guaranteed cost sliding mode controller design for a class of linear uncertain systems with state delays. The system may have time-varying parameter uncertainties as well as norm bounded nonlinear uncertainty in dynamic model. Based on Lyapunov stability and linear matrix inequality (LMI) techniques, a sufficient condition is derived to minimize the upper bounded of a quadratic cost function and to guarantee the stability of the closed loop system. The sliding mode controller keeps the system state on the integral sliding surface. Finally, an example is given to illustrate the feasibility of the proposed control methodology.