On almost equitable partitions and network controllability

Abstract

The main contribution of this paper are two new general necessary conditions for controllability of multi-agent networked control systems involving almost equitable partitions, along with an extension of a well-known symmetry condition to weighted digraphs and multi-input broadcast control signals. The new necessary conditions identify leader selections that break all “symmetries” induced by an almost equitable partition, and in particular genuine graph symmetries, but yet induce uncontrollable dynamics. The results are illustrated on non-trivial examples whose controllability properties are fully characterized by these conditions.