Sliding-Mode Control for Uncertain Time-Delay Systems

The problem of sliding-mode control for a class of time-delay systems is considered.There are uncertainties in both state matrices and input matrix.Moreover,the uncertainties in input matrices is mismatched.By using Lyapunov theory,a sufficient condition in terms of linear matrix inequalities(LMIs) is derived such as the asymptotical stability of the closed-loop system is guaranteed.When the LMIs are feasible,the design of both sliding mode control law and sliding surface can be easily obtained via convex optimization.Moreover,state trajectories are attracted onto the specified sliding surface.A simulation is given to illustrate the effectiveness of the proposed method.