Robust discrete-time nonlinear sliding mode controller with plant uncertainties

Abstract

This paper addresses the new control algorithm, by designing the asymptotically stable nonlinear sliding surface with investigation of the states. This proposed algorithm leads to solve the problem of unstable systems, by proving the asymptotic stability of a class of uncertain discrete-time systems. A particular linear transformation is being defined to transform the discrete-time system and asymptotic stability is proved for designed nonlinear sliding surface, which leads to show stability of the system. The states of the plant’s will be brought down on a proven asymptotic stable nonlinear sliding surface by the proposed control law and they will be remained on stable nonlinear sliding surface for all future times. This proposed technique will be more useful for enhancing the stability of the real world nonlinear systems. The application of proposed algorithm in magnetic tape drive-servo motors and avionic systems, where the parametric uncertainties are occurring frequently.

Keywords: Discrete-time system, linear matrix inequality (LMI), nonlinear system. nonlinear sliding surface, sliding mode control