Robust H₂/H_∞ group consensus control for linear clusters over signed digraphs

In this paper, we investigate H₂/H_∞ group consensus problems for multi-agent systems with general linear dynamics over directed signed graphs. The systems are subject to power bounded noises and spectrum bounded noises. We give a distributed protocol with coupling strengths and a feedback gain matrix to be determined. By using algebraic graph theory, matrix theory and mixed H₂/H_∞ theory, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to guarantee the group consensus performance. Furthermore, to address the problems that the coupling strengths are usually larger than expected and the global structure information may not be used for each agent, two adaptive strategies are proposed such that group consensus can be achieved in a fully distributed fashion. By using these adaptive strategies, not only can the consensus error and the adaptive coupling strengths be ultimately bounded in the presence of disturbances, but also the H₂/H_∞ group consensus can be almost achieved. Finally, some numerical examples are given to illustrate the effectiveness of our proposed approach.