Local synchronization of nonlinear dynamical networks with hybrid impulsive saturation control inputs

Abstract Under the hybrid impulsive control with actuator saturations, this paper studies the local synchronization problem of a class of nonlinear dynamical networks. However, the discontinuity caused by the impulsive effect and the saturation nonlinearity caused by the actuator saturation have brought great challenge to the theoretical analysis of such problems. Firstly, this paper uses mathematical induction to estimate the admissible set of the system state at the impulse instant, which is used to ensure that the saturation nonlinear problem can be dealt with by the sector nonlinear model method and the polyhedral representation method. Secondly, by constructing a suitable time-dependent Lyapunov-Krasovsknii functional (LKF), using Jensen’s inequality, Wirtinger-based inequality and the sector nonlinearity model approach, a sufficient condition has been derived, which guarantee the exponential stability of the synchronization error system in terms of linear matrix inequalities (LMIs). Thirdly, some synchronization criteria are obtained by using polytopic representation approach to deal with the saturation nonlinearity. Based on these criteria, the saturated impulsive and sampled-data controller is designed, and the region of attraction of the drive response error system is estimated. As a corollary, exponentially synchronization conditions and controller design are also presented for the nonlinear dynamical networks without actuator saturation. Finally, two numerical examples shows the effectiveness of the obtained results.