Optimal sliding mode controller for systems with mismatched uncertainty

This paper proposes an optimal sliding mode controller for linear systems affected by mismatched uncertainty. The optimal control law is based on simple linear quadratic technique and the sliding surface is designed by using the linear matrix inequality method. The proposed controller is applied for stabilizing single input single output as well as multi input multi output systems. Simulation results prove that the proposed controller is capable of reducing the control input while offering better transient performances. Moreover, the proposed controller reduces chattering in the control input.