Distributed finite-time control for Markovian jump systems interconnected over undirected graphs with time-varying delay

• Published in: IET control theory & applications Vol. 13; no. 18; pp. 2969 - 2982
• Main Authors: Xue, Xiaojuan, Xu, Huiling, Xu, Li
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 17.12.2019
• Subjects: closed loop systems; closed‐loop system; contractiveness; control problem formulation; control system synthesis; delays; feedback; finite‐time boundedness; finite‐time control; finite‐time interval; finite‐time stability analysis; linear matrix inequalities; Lyapunov methods; Markovian jump systems; mode‐dependent distributed dynamic output feedback controller; nonlinear control systems; nonlinear matrix inequalities; Research Article; stability; stochastic systems; sufficient condition; time‐varying delay; time‐varying systems; uncertain systems; undirected graphs; time-varying systems; time-varying delay; uncertain systems; finite-time control; control problem formulation; mode-dependent distributed dynamic output feedback controller; control system synthesis; nonlinear matrix inequalities; feedback; closed loop systems; finite-time boundedness; linear matrix inequalities; nonlinear control systems; delays; finite-time stability analysis; stochastic systems; Markovian jump systems; contractiveness; finite-time interval; sufficient condition; undirected graphs; stability; closed-loop system; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5879

This study considers the problems of stochastic finite-time stability analysis and distributed finite-time control for Markovian jump systems interconnected over undirected graphs with time-varying delay. First, the concepts of the well-posedness, stochastic finite-time boundedness and contractiveness for the class of systems are introduced, and the control problem formulation is presented. Then, a sufficient condition on the well-posedness, stochastic finite-time boundedness and contractiveness for the resulting closed-loop systems is proposed by a set of non-linear matrix inequalities in some given finite-time interval. For decoupling this non-linearity, a sufficient condition on the existence of a mode-dependent distributed dynamic output feedback controller is established in terms of linear matrix inequalities with some fixed parameter. Moreover, the obtained controller, which not only inherits the structure of the plant but also has the same jumping process as the plant, can guarantee that the closed-loop system is stochastic finite-time bounded and contractive in some given finite-time interval. Furthermore, an algorithm is presented to obtain the parameters of such controllers. Finally, a numerical simulation is presented to show the validity of the proposed method.