Integral sliding mode control for systems with time-varying input and state delays

This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with time-varying state and input delays. An integral sliding surface is firstly constructed. Then, by using the Lyapunov-Krasovskii functional and some specified matrices, a sufficient condition is obtained in the form of linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be asymptotically stable. Furthermore, a sliding mode controller law is synthesized to guarantee that the system trajectories can be driven onto the specified sliding surface in a finite time and maintained there for all subsequent time. Finally, an inverted pendulum model is used to illustrate the advantages and effectiveness of the design method.