H∞ consensus for nonlinear stochastic multi-agent systems with time delay

This paper is concerned with the problem of H∞ consensus for nonlinear stochastic multi-agent systems with time-delay. The objective is to design a dynamic output feedback protocol such that the multi-agent system reaches consensus in mean square and has a prescribed H∞ performance level. First, by transforming models, the H∞ consensus problem is converted to a standard H∞ control problem. Then, by using the Lyapunov-Krasovskii functional method and the generalized Itô's formula, both delay-independent and delay-dependent stochastic bounded real lemmas are developed. Based on these, sufficient conditions on the existence of the desired dynamic output feedback protocol are presented in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.