Sliding mode control for discrete-time singular semi-Markovian jumping models

Abstract

In this paper, the sliding mode control (SMC) is studied for discrete-time uncertain singular semi-Markovian jumping models. The aim is to construct an appropriate SMC strategy such that the stochastic admissibility conditions in the form of strict linear matrix inequalities are established for the corresponding closed-loop system under the framework of the semi-Markovian jumping process. Firstly, considering the particularity of singular systems, a common sliding surface with the singular matrix is designed, which can effectively reduce the influence of repetitive jumping among subsystems on the sliding surface and the numerical problem caused by the existence of the singular matrix. Then, in line with an improved reaching condition, the desired SMC mechanism is synthesized to drive the system state onto the pre-designed sliding surface. Finally, the DC motor model is taken as an example to demonstrate the effectiveness of the proposed SMC approach.