Sliding mode control of phase-type T-S fuzzy stochastic semi-Markov jump systems

Abstract

In this paper, the sliding mode control (SMC) problem of phase-type semi-Markov jump systems (S-MJSs) is studied using Takagi-Sugeno (T-S) fuzzy technology. A novel integral-type sliding surface with artificial delay has been constructed and applied for the first time to phase type S-MJSs, reducing system conservatism and enhancing control performance. Firstly, this paper presents sufficient criteria for the robust random stability of these systems by utilizing model transformation methods, supplementary variable techniques, and modal-dependent Lyapunov-Krasovskii function methods. Secondly, the sliding mode controller is designed using matrix technology. Finally, the effectiveness of this method is demonstrated through a simulation example involving a single-link robotic arm, and the comparison results show the merits to the existing achievements.