Delay-dependent adaptive sliding mode control of uncertain systems with state and input delays

This paper is concerned with the robust stability and robust stabilization for a class of uncertain systems with delayed state and control. Introducing an extra time-delay term in system and taking the relationship between the terms in the Leibniz-Newton formula into account obtain a new delay-dependent stability criterion. Based on this stability criterion, firstly a sufficient condition is proposed for existence of the sliding mode in terms of linear matrix inequalities. Correspondingly, a sliding mode controller is also synthesized for the reaching motion. Moreover, an adaptive law is introduced to adaptively estimate the unknown external disturbances resulted by the system transformation. The control strategy guarantees the robust asymptotic stability of the closed-loop system. A numerical example is included to demonstrate the effectiveness of this control scheme.