Sliding mode controller design for linear time delay systems

The present results deal with the stabilization of linear delay systems. Stabilizing control laws proposed are of discontinuous type and constitute the main contribution of the paper. A "toolbox" used in the control synthesis is based on conversion of a state representation to a regular form and on a new delay-dependent stability criterion. Different discontinuous unit controllers ensuring the global asymptotic stability are developed. By using an appropriate Lyapunov-Krasovskii functional, the control algorithms are proven to be robust with respect to matching disturbances with apriori-known upperbounds. Also, admissible upperbounds for the delay is derived. The study is supported by an example.