Controllability of second-order multi-agent systems with impulse-effected switching topologies

This paper studies the controllability of second-order multi-agent systems with impulse-effected switching topologies. By employing the relative protocol, the second-order multi-agent systems under impulse-effected switching topologies are transformed into a second-order impulsive switched system. Analytical solution of the switched system is derived by constructing some novel nested functions. On this basis, we establish a set of necessary and sufficient controllability criteria, which demonstrate that controllability of the multi-agent systems with impulse-effected switching topologies is fundamentally determined by the interaction topology of each subsystem, the switching sequence and the impulse gain. Furthermore, we derive some specific controllability characteristics for various system categories, which elucidate the fundamental distinctions and intrinsic connections among impulsive switched systems, switched systems, impulsive systems, and conventional linear systems. A numerical example is provided to illustrate the effectiveness of the derived controllability criteria.