Swarm Stability of Compartmental Networks with Linear Time-Invariant High-Order Dynamical Protocol

Abstract

Swarm stability is concerned for compartmental networks with linear time invariant high-order dynamical protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient condition of swarm stability is given, which requires that the products of nonzero elements from the spectrum of the Laplacian matrix of the network and the spectrum of the dynamical protocol possess nonnegative real parts. Two numerical instances are illustrated.