Controllability of multi-agent systems with time-delay in state and switching topology

Abstract

In this article, the controllability issue is addressed for an interconnected system of multiple agents. The network associated with the system is of the leader–follower structure with some agents taking leader role and others being followers interconnected via the neighbour-based rule. Sufficient conditions are derived for the controllability of multi-agent systems with time-delay in state, as well as a graph-based uncontrollability topology structure is revealed. Both single and double integrator dynamics are considered. For switching topology, two algebraic necessary and sufficient conditions are derived for the controllability of multi-agent systems. Several examples are also presented to illustrate how to control the system to shape into the desired configurations.

Keywords:

• controllability
• multi-agent system
• single-integrator
• double-integrator
• switching topology
• state delay

Acknowledgements

This work was supported by the Royal Society K.C. Wong Education Foundation Postdoctoral Fellowship of the United Kingdom and the National Natural Science Foundation of China (Nos. 60604032, 10601050, 60704039).