Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays

This paper investigates the switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays on undirected networks, in which both a single time-delay and multiple time-delays are addressed. It is established that the switching controllability of discrete-time multi-agent systems is only determined by the information from the leaders to the followers, and the discrete-time multi-agent systems are controllable even if each of its subsystems is uncontrollable. For the special case of fixed topology, an equivalent augmented system without time-delays is proposed to analyze the controllability of multi-agent systems via PBH rank test. Some numerical examples are provided to demonstrate the effectiveness of the theoretical results.