Consensus Control of Discrete-Time Multiagent Systems Over Correlated Fading Channels: A Compressed Coding Scheme

This article focuses on the mean-square consensus control problem for a class of discrete-time multiagent systems (DT-MASs) over time-correlated multistate Markovian fading channels, where the packet loss probability is time-varying and depends on the current channel state. In order to save limited network bandwidth, a compressed coding scheme is developed by preprocessing the measurement output. With the aid of a stochastic Lyapunov-Krasovskii functional, a sufficient condition is first obtained under which the consensus error system is mean-square stable for DT-MASs over identical fading channels. Then, the consensus gain is formulated as the feasible solution to a set of linear matrix inequalities (LMIs) whose dimensions are independent of the number of agents. Furthermore, for the case that agents communicate over nonidentical fading channels, the mean-square consensus problem is transformed into an analyzable edge agreement issue in the mean-square sense by means of properties of the edge Laplacian combined with a mapping technique. Next, a sufficient condition is derived to ensure the mean-square consensus performance, based on which the existence of the controller can be guaranteed by the feasibility of a set of LMIs. Finally, the validity and feasibility of the developed design scheme are shown by two illustrative examples.