Diagonal stability for a class of graphs with connected circles

Diagonal stability for a class of matrices having strongly connected graphs is considered, in which each pair of distinct simple circles have at most one common edge or a common vertex. We apply the obtained results to analyze stability of a class of nonlinear dynamical networked systems, for which each subsystem is output strictly passive and the storage function is available. We show that diagonal stability of the dissipativity matrix that includes the information of interconnection structure of subsystems implies that the sum of weighted storage functions is a storage Lyapunov function for this class of networks.