This article studies the $H_{\infty }$ exponential synchronization problem for complex networks with quantized control input. An aperiodic sampled-data-based event-triggered scheme is introduced to reduce the network workload. Based on the discrete-time Lyapunov theorem, a new method is adopted to solve the sampled-data problem. In view of the aforementioned method, several sufficient conditions to ensure the $H_{\infty }$ exponential synchronization are acquired. Numerical simulations show that the proposed control schemes can significantly reduce the amount of transmitted signals while preserving the desired system performance.

This paper is devoted to investigating the impact of the recurrence of rumors and individual behaviors and control strategies related to rumor spreading in online social networks. To do this, a novel susceptible-hesitating-infected-latent-recovered (SHILR) rumor propagation model in heterogeneous networks is presented. Firstly, based on the relevant mean-field equations of the model, the threshold value is examined to demonstrate the existence and stability of rumor-free/spreading equilibrium with the help of the algebraic method. Secondly, the global stabilities of the equilibria are analyzed through applying Lyapunov stability theory and LaSalle’s invariance principle. Next, the optimal control is proposed by taking advantage of Pontryagin’s maximum principle for reducing the number of infected individuals with minimum cost. Moreover, some numerical examples are carried out to test the theoretical results. Finally, combined with practice, a model application is presented.