Adaptive output synchronization of complex delayed dynamical networks with output coupling

In the present paper, two kinds of adaptive output synchronization problems for a complex delayed dynamical network with output coupling are investigated, that is, the cases with positive definite output matrix and with semi-positive definite output matrix. For the former, by using adaptive control method, a sufficient condition is obtained to guarantee the output synchronization of the complex dynamical network. In addition, a pinning adaptive output synchronization criterion is also derived for such network model. Then we extend these results to the case when the output matrix is semi-positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.