Sliding mode control for a class of linear mismatched uncertain systems

A method of sliding mode controller is presented to a class of linear mismatched uncertain systems based on integral sliding mode and rate reaching law. Firstly, the existence of equivalent controller is guaranteed. The unmatched is will not be amplified by the discontinuous control. In order to reduce chattering, a bipolar sigmoid function without high frequency switching is induced. The controller based on integral sliding mode and rate reaching law stability is ensured using the Lyapunov method. It has better performance in stationarity and robustness. An example is given to show the effectiveness of the developed approach.