Suboptimal Output Consensus for Time-Delayed Singular Multi-Agent Systems

The current paper investigates guaranteed-cost output consensus analysis and design problems for high-order linear time-invariant singular multi-agent systems with constant time delays, which can realize suboptimal output consensus control. Firstly, a new output consensus protocol with a suboptimal index and a single delay is proposed to realize the tradeoff design between output consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed-cost output consensus and consensualization are derived in terms of linear matrix inequalities by a combined tool from the Lyapunov-Krasovskii approach and the free-weighting matrix technique, respectively, and the output consensus function is determined on the basis of the First Equivalent Form. Finally, a numerical example is performed to demonstrate the effectiveness and conservativeness of theoretical results.