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

Abstract

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.