Abstract: This paper is concerned with the pinning synchronization problem of complex networks. By defining a new nonlinear $P$-measure of the nonlinear operator, a set of sufficient conditions are obtained to guarantee the global synchronization of the pinning process. The obtained results do not require the symmetric irreducibility of the coupling matrix and the continuous differentiability of functions. Therefore a broader application domain for the pinning synchronization of complex networks is provided. Finally, two simulation examples of complex networks are presented to demonstrate our theoretical results.

Key words: nonlinear measure, complex network, pinning synchronization