Design of sliding mode control for multi-input systems with multiple state delays

In this paper, the design problem of a sliding mode controller for multi-input systems with several delays is investigated. A new control law is proposed. The sufficient conditions for the existence of a sliding mode are derived. The result are given in terms of matrix norm inequalities. We have developed some constructive delay-independent conditions for the asymptotic stability of multivariable system with multiple state delays based on Lyapunov-Krasovskii functional combined with linear matrix inequalities techniques. By these conditions we have successfully designed a new sliding mode control law for the stabilization of multi-input system with several delays. The sliding and stability conditions are less conservative than existing conditions.