Sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of a sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. The coefficient matrix of the sliding function can be designed to satisfy a new matching condition provided time-varying uncertainties are bounded. It is shown that the system is invariant on the sliding surface. It is also shown that the stability of the closed-loop system is guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controller.