Mean Square Consensus of Multi-Agent Systems Over Non-Identical Delayed and Fading Channels

This paper addresses the mean square consensus problem in a multi-agent system (MAS) operating over a directed graph that encounters non-identical transmission delays and non-identical fading channels. Notably, the presence of non-identical delays poses challenges to directly modeling the error within the MAS. To circumvent this issue, we introduce a novel approach following discretization, where we establish predefined controller update intervals equal to the maximum delay, yielding an equivalent delay-free MAS. Then, we derive an error model whose mean square stabilization problem is ultimately equivalent to the mean square consensus issue of the original MAS, utilizing edge dynamics. Based on this framework, we present a sufficient condition for achieving consensus within the MAS. Finally, a numerical simulation example is demonstrated to verify our proposed results.