Stabilizability of a group of single integrators and its application to decentralized formation problem

This paper addresses a fundamental property for a class of multi-agent systems, i.e., stabilizability of a group of single integrators, having external control inputs, under a fixed and weighted directed network topology. A necessary and sufficient condition for the stabilizability of the multi-agent system is presented. In particular, it is shown that the multi-agent system is stabilizable if and only if the external control inputs are applied to certain agents (e.g., root node of the communication network when the network is connected). The framework proposed here puts an emphasis on its ability in decentralized control; that is, each agent uses its own and its neighbors´ state information as feedback, to stabilize the multi-agent system. Based on these results, the decentralized set-point control problem with formation is also addressed.