Group controllability of discrete-time multi-agent systems

Controllability is a fundamental issue concerning control of multi-agent networks and a very important research topic in the modeling, analysis and coordination control of multi-agent systems. Group controllability problem is a further extension of the controllability problem of the general multi-agent systems, which mainly studies the cooperation and control of multi-agent systems with multiple sub-groups or multiple intelligence clusters. Comparing with the controllability of the general multi-agent systems, the group controllability is not only to consider the information interaction among the groups, but also to consider the information interaction between different groups, which makes the system reflect the effect of a whole and also the internal structure of the sub-groups. This paper addresses the group controllability problems of discrete-time multi-agent systems with time-delay, in which both switching topology and fixed topology are considered. This paper also proposes the general definition of the group controllability, as well as establishes group controllability criteria from the algebraic and graphical perspectives. Numerical examples and simulations are proposed to illustrate the theoretical results.