Lag output synchronization for multiple output coupled complex networks with positive semidefinite or positive definite output matrix

This paper investigates the lag output synchronization of a multiple output coupled complex network, in which the output matrix is positive semidefinite or positive definite. By selecting an appropriate output feedback controller and Lyapunov functional, a criterion is acquired to insure the lag output synchronization for the complex network, in which the output matrix is positive definite. Moreover, an adaptive output feedback control strategy is also developed for ensuring the lag output synchronization in the network with positive definite output matrix. On the other side, we also similarly study the case of positive semidefinite output matrix. Lastly, two numerical examples are given to demonstrate the came up with criteria.