Chattering-free grey sliding mode control for discrete time-delay systems with unmatched uncertainty

According to a class of discrete time-delay systems with unmatched uncertainties and disturbance, a new chattering free least squares support vector machine grey sliding mode control (LS-SVM-GSMC) law based on Linear Matrix Inequality (LMI) is presented. Estimated value of external disturbance is obtained by grey model, and output of LS-SVM is used for replacing sign function of the reaching law in grey sliding mode control (GSMC). The feasibility and effectiveness of the LS-SVM-GSMC scheme are demonstrated via numerical examples. As a result, by adopting LS-SVM-GSMC, chattering which is caused by grey reaching law is eliminated, and effect of unmatched disturbance is reduced.