Consensus For Time-Delay Multi-Agent Systems With H-Infinity Performance In Finite Frequency Domains

This paper considers the problem of robust control synthesis such that time-delay multi-agent systems are consensus and capture the finite frequency domain performance. Using a linear transformation, the consensus problem is first transformed into a partial stability problem. Then, based on a dual version of generalised Kalman-Yakubovich-Popov (GKYP) lemma and a partial multiplier expansion method, new sufficient conditions guaranteeing the existence of static output feedback controller are proposed in terms of linear matrix inequalities (LMIs) without introducing conservatism. Finally, the effectiveness of the presented method is illustrated via a two-cart-one-spring system and a numerical example.