Design of topology switching law for formation problem of linear multi-agent systems with time-varying delay

This paper investigates the formation problem for high-order continuous-time multi-agent systems with time-varying delay under switching communication topologies. The communication topology of multi-agent systems switches within a finite set of digraphs which depicts the communication structure between agents. One case of topology set is considered: there does not exist a directed spanning tree for each of the topologies but there exists a directed spanning tree for the union of all the topologies. By a linear transformation, the formation problem is transformed into stability analysis of a switched delay systems. With the help of a stabilizing switching law, sufficient conditions for multi-agent systems to achieve a given formation under switching topologies are presented in terms of linear matrix inequalities (LMIs). A formation example of intelligent vehicle system is shown to illustrate the effectiveness of the switching strategies.