Pinning synchronization of a general complex dynamical network

In this letter, we provide a simply approximate formula for estimating the detailed number of pinning nodes and a novel pinning synchronization criteria are obtained for a given general complex dynamical network. By using eigenvalues of the minor matrix of inner- coupling matrix and Schur lemma, we can reduce the gain factor of the controller. Previous results about symmetric coupling matrix are included as special cases of the present work. Finally a network example consists of 10 identical Lorenz systems are given to show the effectiveness of the proposed synchronization criteria.