Topology-independent robust stability for networks of homogeneous MIMO systems

Abstract

We study dynamic networks described by a directed graph where the nodes are associated with MIMO systems with transfer-function matrix F(s), representing individual dynamic units, and the arcs are associated with MIMO systems with transfer-function matrix G(s), accounting for the dynamic interactions among the units. In the nominal case, we provide a topology-independent condition for the stability of all possible dynamic networks with a maximum connectivity degree, regardless of their size and interconnection structure. When node and arc transfer-function matrices are affected by norm-bounded homogeneous uncertainties, the robust condition for size- and topology-independent stability depends on the uncertainty magnitude. Both conditions, expressed as constraints for the Nyquist diagram of the poles of the transfer-function matrix H(s) = F(s)G(s), are scalable and can be checked locally to guarantee stability-preserving “plug-and-play” addition of new nodes and arcs.