Partial Controllability of Discrete-Time Multi-Agent Systems with A Leader and Time-Delay

Generally speaking, the complete controllability of multi-agent systems refers to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole, that is the complete controllability. Comparing with the complete controllability of multi-agent systems, in reality, it may not be necessary to actuate all agents to the desired configuration. This paper concentrates on the partial controllability problems of discrete-time multi-agent systems with a leader and time-delay on the fixed topology, gives the general definition of the partial controllability, establishes partial controllability criteria. Numerical example and simulations are proposed to illustrate the theoretical results.