Distributed Stochastic Control for a Class of Discrete-Time Interconnected Systems With Communication Losses

This article focuses on the problems of analysis and synthesis for a class of discrete-time interconnected systems having random communication losses among subsystems. To deal with distributed control problems for the considered systems, a new model is coupled as a class of Markov jump systems with some structured uncertainty parameters. Then, based on this new model, some sufficient conditions are presented to ensure the required performance in terms of solvable linear matrix inequalities (LMIs). To design an appropriate distributed controller to neutralize the uncertainties, communication losses, and disturbances, a feasible distributed algorithm is developed with respect to the new system model to ensure that the states and performance of the resulting closed-loop system converge to the ideal ones. The derived results are based on stochastic Lyapunov theory and $H_{\infty }$ criterion. Finally, numerical simulations are conducted to validate the proposed algorithms.