Containment control of second-order discrete-time multi-agent systems with Markovian missing data

This study investigates the containment control problem of second-order discrete-time multi-agent systems with Markovian missing data in actuators and one step network-induced time delay. The process of missing data from the controller to the actuator is modelled by a homogeneous, finite-state and discrete-time Markov chain. The authors first discuss the containment control problem for the case when all the elements of the transition probability matrix are completely known, then the result is extended to a more general case with only partially known transition probabilities. The distributed control protocol with one step time delay is proposed. Based on the stochastic Lyapunov-Krasovskii functional method, sufficient conditions in terms of a set of matrix inequalities are given to guarantee that the states of all the followers asymptotically converge to the convex hull formed by the corresponding states of the leaders in mean square sense. A cone complementary linearisation algorithm is used to obtain the control gains. Finally, two numerical simulations are provided to show the effectiveness of theoretical results.