Stability of non-diagonalizable networks: Eigenvalue analysis

Abstract

The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the coupling and control matrix. The dependence of the stability on both pinning density and pinning strength is studied. © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.