In this brief, a sliding mode controller (SMC) established via a new adaptive reaching law is proposed for discrete-time systems. To guarantee a smaller width of the quasi-sliding mode domain (QSMD), disturbance of the system is estimated based on the second-order difference of historical observation information, and the reaching law is designed on the choice of a negative power term that adapts to the variations of the switching function. Dynamics of the controlled system both outside and within the QSMD are analyzed.
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Lin et al. (2019) studied this question.
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