Sliding Mode Control for Nonlinear Stochastic Singular Semi-Markov Jump Systems

• Published in: IEEE transactions on automatic control Vol. 65; no. 1; pp. 361 - 368
• Main Authors: Qi, Wenhai, Zong, Guangdeng, Karimi, Hamid Reza
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control theory; D C motors; Liapunov functions; Markov analysis; Markov processes; Nonlinear control; Nonlinearity; Probability distribution; Semi-Markov jump systems (S-MJSs); Sliding mode control; stochastic disturbance; Switches; Symmetric matrices; Weibull distribution
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2915141

This paper deals with the problem of sliding mode control design for nonlinear stochastic singular semi-Markov jump systems (S-MJSs). Stochastic disturbance is first considered in studying S-MJSs with a stochastic semi-Markov process related to Weibull distribution. The specific information including the bound of nonlinearity is known for the control design. Our attention is to design sliding mode control law to attenuate the influences of uncertainty and nonlinear term. First, by the use of the Lyapunov function, a set of sufficient conditions are developed such that the closed-loop sliding mode dynamics are stochastically admissible. Then, the sliding mode control law is proposed to ensure the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity of the proposed method.