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

Abstract

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.