Robust fuzzy integral sliding mode control of the linear mismatches systems

An adaptive fuzzy integral sliding mode controller for mismatched time-varying linear systems is presented in this paper. The integration of error is included in the sliding function to have the system steady state error become zero. The sliding coefficient matching condition is extended for the integral sliding mode control. The proposed fuzzy integral sliding mode controller is designed to have zero steady state system error under step inputs and alleviate the undesired chattering around the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy integral sliding mode control system. It is not required to know the bounds of the uncertainties in advance for the presented adaptive fuzzy integral sliding mode controller. Also, the designed fuzzy integral sliding mode control system is shown to be invariant on the sliding surface. Moreover, the reaching mode of the sliding surface is guaranteed and the close-loop system is stable. Simulation results are included to illustrate the effectiveness of the presented fuzzy integral sliding mode controller.