Variable structure control of time-delay systems with retarded state and retarded control

In this paper, some new types of stability theorems are obtained for time-delay systems described by retarded functional differential equations (RFDEs). A design approach to the sliding mode control of time-delay systems with retarded state and retarded control is given. By introducing proper dynamic compensators, simple equivalent control law is obtained and the motion equations of sliding modes are obtained. By using the new stability theorem for RFDEs, a stability theorem for the sliding mode motions is established. The design method of this paper can be applied to make the controlled systems not only achieve strong robustness but also good dynamic performance by using the variable structure control law