Synchronization of Heterogeneous Partially Coupled Networks with Heterogeneous Impulses

This paper discusses quasi-synchronization problem in an array of heterogeneous partially coupled dynamical networks. At first, based on the Lyapunov stability theorem and the comparison principle, sufficient quasi-synchronization criteria are presented such that the proposed heterogeneous partially coupled dynamical networks with heterogeneous impulses can be synchronized within a nonzero error bound. Then, by taking a specific matrix function, we obtain some lower-dimensional inequalities, which are easy to be verified. Moreover, we propose the design method of controllers under a given error bound and study the optimization problem for the error bound. Finally, a numerical example is provided to illustrate the efficiency of the obtained results.