Optimal sliding mode disturbance rejection for systems with delayed state and control input

This paper is concerned with the problem of optimal sliding mode disturbance rejection for linear systems with delayed state and control under disturbances. Based on a model transformation, the system with delayed state and control input under disturbances is transformed into a system only with state delay. By using the successive approximation approach, an optimal sliding surface and an optimal sliding control law are designed. The designed optimal sliding control law ensures that the dynamic performance of the closed-loop system is optimal, at the same time the stability of the system is ensured. A numerical simulation is employed to verify the effectiveness of the proposed approach.