Controllability of Two-Time-Scale Discrete-Time Multiagent Systems

In this paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results.