Graph-theoretic characterisations of zeros for the input–output dynamics of complex network processes

Abstract

We examine linear network dynamics in which an input can be applied at only one network component and measurements can only be made at one (in general different) component. The infinite-zero and finite-zero structures of these dynamics are characterised explicitly in terms of the network's graph matrix, using the special coordinate basis for linear system. These algebraic characterisations are then used to identify relationships between features of the network's graph topology and the state matrix of its finite zero dynamics.

Keywords:

• synchronisation/diffusion processes
• sparse control of networks
• special coordinate basis
• graph-theory

Additional information

Funding

This work was partially supported by the United States National Science Foundation [grant number ECS-0901137] and [grant number CNS-1058124].