Quasi-synchronization of complex dynamical networks with switched coupling strengths based on a generalized Halanay’s inequality

Abstract

This paper investigates the exponential quasi-synchronization problem of complex dynamical networks with switched coupling strengths. First, a generalized Halanay’s inequality has been established, which further extends the existing result in Mazenc et al. This inequality not only allows the gain to surpass the decay rate but also helps to cope with quasi-synchronization of complex dynamical networks with switched coupling strengths. Then, in virtue of the obtained inequality, Lyapunov function, and some other important inequalities, sufficient criteria ensuring the quasi-synchronization for the considered system are derived analytically. A numerical example is provided to verify the feasibility of the results.