Composite anti‐disturbance control for semi‐Markovian jump systems with time‐varying delay and generally uncertain transition rates via disturbance observer. Issue 14 (18th August 2020)

• Record Type: Journal Article
• Authors: Xu, Tianbo; Gao, Xianwen; Pang, Guochen; Qi, Wenhai; Kao, Yonggui
• Is Part Of: IET control theory & applications. Volume 14:Issue 14(2020)
• Page Start: 1877
• Page End: 1887
• Publication Date: 2020-08-18
• Subjects: Lyapunov methods -- linear matrix inequalities -- closed loop systems -- uncertain systems -- control system synthesis -- delays -- stability -- time‐varying systems -- observers -- Markov processes -- stochastic systems -- nonlinear control systems; composite antidisturbance control -- semiMarkovian jump systems -- time‐varying delay -- generally uncertain transition rates -- disturbance observer -- S‐MJS -- multiple disturbances -- system performance level -- composite control system -- disturbance suppression level -- mode‐dependent time‐delay problem -- composite controller -- antidisturbance control problem -- disturbance‐observer‐based system; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2019.0833
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : The problem of composite anti‐disturbance control for semi‐Markovian jump systems (S‐MJSs) with time‐varying delay via disturbance observer is analysed in this study. Unlike the existing methods, generally uncertain transition rates, time‐varying delay, multiple disturbances, the H ∞ performance and disturbance‐observer‐based control (DOBC) are all considered in S‐MJSs. The method which combines DOBC and H ∞ control is used to guarantee the system performance level of time‐varying delay S‐MJSs. Firstly, a sufficient condition of stochastic stability in the H ∞ performance level for the composite control system is given by using piecewise Lyapunov–Krasovskii functional. Secondly, the optimal value of disturbance suppression level for the system is solved by an optimisation algorithm. Thirdly, variation interval of time‐delay has been divided into equal small intervals for reducing the conservatism of the method which addresses the mode‐dependent time‐delay problem. Furthermore, the composite controller and disturbance observer which satisfy the proposed stability condition are designed to address the composite anti‐disturbance control problem of the closed‐loop system. Finally, two practical systems are provided to testify the accuracy of research methods.