Stabilisability of discrete-time multi-agent systems under fixed and switching topologies

This paper studies the problem of stabilisability for general discrete-time linear multi-agent systems. For fixed topology, a necessary and sufficient graph-theoretic condition is proposed. Based on this, a general linear form of the external control input is given, and two methods to design the feedback gain matrix by Riccati equality/inequality are given. For switching topology, a sufficient graph-theoretic condition is presented, under which the stabilisability of multi-agent systems is achieved by introducing an averaging analysis approach. Additionally, both results under fixed and switching topologies are applied for solving the tracking and formation control of discrete-time multi-agent systems, and some sufficient and/or necessary conditions are presented. Finally, numerical examples are given to illustrate the theoretical results.