Leader-follower guaranteed-cost consensualization for high-order linear swarm systems with switching topologies

Leader-follower guaranteed-cost consensus analysis and design problems for high-order linear time-variant swarm systems with switching topologies are investigated, where two types of switching topologies are considered; that is, each interaction topology in the switching set has a spanning tree, and the union of a series of interaction topologies in a certain time interval has a spanning tree, which is referred to a joint spanning tree. Firstly, the leader-follower guaranteed-cost consensus problem is introduced, which means that all the followers in a swarm system can track the state of the leader and some performance index should be satisfied simultaneously; that is, leader-follower consensus is achieved in a suboptimal manner. Secondly, by the state decomposition, a necessary and sufficient condition for leader-follower consensus is proposed, which only transforms leader-follower consensus problems into asymptotic stability ones but cannot be directly used to determine whether or not swarm systems can achieve leader-follower consensus. Furthermore, in terms of linear matrix inequalities, sufficient conditions of leader-follower guaranteed-cost consensualization for swarm systems with a spanning tree and a joint spanning tree are presented respectively. Finally, two numerical examples are given to demonstrate theoretical results.