Nonlinear quasi sliding mode robust control for discrete time systems with time delay
The robust sliding mode control is investigated for a class of discrete time systems with time varying delay,which is based on a novel nonlinear time varying quasi sliding surface design scheme.Firstly,the general form of the nonlinear switching function with time varying feature is given,which can dynamically improve the quality of its motion.By using the free weighting matrix and linear matrix inequality technique,we propose a design method for the nonlinear quasi sliding surface,and obtain a sufficient condition of asymptotical stability for the nonlinear sliding motion.Secondly,the quasi sliding mode controller is designed based on the improved discrete reaching law to ensure the state of the system for reaching the quasi sliding mode in a finite time.Thus,the quasi sliding mode variable structure control(VSC) for such nonlinear system is extended to the nonlinear control with time delay.Simulation validates that the dynamic behavior of the system is stable with rapid response,low overshoot,less settling time,when employing the proposed quasi sliding surface and quasi sliding mode VSC.