Abstract:

For a class of mismatched uncertain multiple input multiple output linear systems with state time delay, a new selftuning sliding mode control method is proposed based on the linear matrix inequality theory. In this method a sufficient condition for the existence of linear sliding surface is given according to the linear matrix inequality theory, while in the sliding phase such that the system is restricted to the switch surface and completely invariant to mismatched uncertainties and state time delay. For controller output chattering case, the Sigmoid function instead of sign function is introduced and a selftuning sliding mode controller is further designed. Under the selftuning law, the Sigmoid function’s boundary layer and switching gain can be adjusted automatically, which can reduce the high frequency chattering of outputs. The Lyapunov theory is applied to prove the stability of this new control method. Finally, the simulation results of an example are investigated to show the feasibility and effectiveness of the proposed approach.