Adaptive sliding mode control for uncertain systems with state time-delay and known external disturbances

For a class of matched uncertain MIMO linear systems with state time-delay and the known external disturbances, an adaptive sliding mode control method was proposed based on the linear matrix inequality theory. A sufficient condition for the existence of linear sliding surface was given in terms of linear matrix inequality. When into the sliding mode, system was restricted to the sliding surface and completely invariant to matched uncertainties and state time-delay. For controller output chattering case, the sigmoid function instead of sign function was introduced and an adaptive sliding mode controller was further designed. Under the adaptive laws, boundary layer and switching gain of the sigmoid function can be adjusted adaptively, which can reduce the high frequency chattering of outputs. The stability of this control method based on Lyapunov theory was proved. Finally, the simulation results of an example which about the intelligent vehicle's lane keeping was investigated to show the feasibility and effectiveness of this control method.