Design of robust adaptive sliding mode controller for uncertain nonlinear discrete-time systems

In this article, the problem of sliding mode control (SMC) for uncertain discrete-time systems is investigated. The matched uncertainties in the state matrix are norm-bounded and can be estimated by the adaptive approach. Two situations are considered in this text: the state is measurable, and the state is unmeasurable. We chose an appropriate sliding surface such that the trajectories of states will lie in the sliding surface from the initial time. The conclusion is derived that the the siding mode dynamics are asymptotic stability according to the linear matrix inequalities (LMIs) approach. At last, two simulation examples are shown to express the advantages of the technique in this article.