Quasi-synchronization of heterogeneous Lur'e networks with uncertain parameters and impulsive effect.

• Heterogeneous networks with both heterogeneous coefficients and heterogeneous nonlinear functions are investigated. • A generalized impulsive controller is designed. • Parameter uncertainties of both linear and nonlinear dynamics are considered. • The sufficient criteria of quasi-synchronization are derived for the heterogeneous networks. The target of this paper is studying the problem of quasi-synchronization of heterogeneous Lur'e networks with uncertain parameters and impulsive effect. Considering the heterogeneity of Lur'e networks, quasi-synchronization instead of synchronization is discussed. Noting that the uncertain factors exist extensively in reality, uncertain parameters are introduced to the system in this paper. By using the Schur complement lemma, stability theory and the principle of comparison, the sufficient criteria for the heterogeneous networks to achieve quasi-synchronization are derived, and the upper bound of exponential quasi-synchronization errors is calculated. In addition, two corollaries are presented in consideration of homogeneous systems and weighted undirected graphs. Finally, three numerical simulations are given to illustrate the effectiveness of the control protocol and theoretical results. [ABSTRACT FROM AUTHOR]