Sliding mode control for linear uncertain systems with input and state delays

The problem of designing sliding mode controllers for a class of linear systems with uncertainties and both input and time state delays is investigated. A particular linear transformation is defined to transform the time-delay system into a delay-free form first. Then, the sliding mode controller is designed based on the transformed system. Optimal control theory is adopted to construct the optimal sliding manifold with a quadratic performance index minimized. The selected control law can ensure the existence of the sliding mode and alleviate chattering effectively in the sliding motion. About the uncertainties, the cases of matched condition and unmatched condition are studied respectively. Furthermore, a sufficient condition that guarantees the global asymptotic stability of the original system is derived. Finally, a numerical example is given to illustrate the proposed approach.