Guaranteed-Cost Consensus for Singular Multi-Agent Systems With Switching Topologies

Guaranteed-cost consensus problems for high-order singular multi-agent systems with switching topologies are investigated. Firstly, to achieve a trade-off design object between consensus regulation performances and control energy consumptions, a quadratic cost function is constructed by state errors among agents and control inputs of all agents and guaranteed-cost consensus problems are introduced. Then, based on linear matrix inequality techniques, sufficient conditions for guaranteed-cost consensus and consensualization are presented respectively, which can guarantee the scalability of singular multi-agent systems since the dimensions of all the variables in these conditions are independent of the number of agents. Moreover, an upper bound of the cost function is determined, explicit expressions of consensus functions are given on the basis of the Second Equivalent Form, and it is shown that consensus functions are dependent on the average of initial states of all agents but are independent of switching topologies. Finally, the applications of theoretical results in multi-agent supporting systems are shown.