Analysis of Pinning-Controlled Networks: A Renormalization Approach

In this paper, a renormalization approach is introduced for analyzing pinning-controlled networks. The renormalization process consists of two operations, edge weighting and node reduction, and is built on a new concept of passivity comparison in the sense of Lyapunov V-stability. Furthermore, a cascaded model resulted from the renormalization process in a layer structure is presented for estimating the $V$ -stability of a network. Finally, simulation studies are presented for illustration and verification of the theoretical results.