Quasi-synchronization of heterogeneous networks with Lévy noise and semi-Markov jump via intermittent delay sampled-data control

Abstract

We mainly study the quasi-synchronization problem of heterogeneous networks in the presence of Lévy noise and semi-Markov jumps. In terms of controller design, we propose two schemes: one is intermittent delay sampled-data control, and the other is time-varying intermittent delay sampled-data control. Both schemes are based on intermittent delay control and integrate the characteristics of time-varying gain and state sampling. Different from the previous continuous and uninterrupted sampling control, their significant advantage lies in the adoption of discrete data sampling, which improves efficiency and saves costs to a certain extent. Among them, the time-varying intermittent delay sampled-data control further enhances the adaptability to complex dynamic environments by dynamically adjusting the control gain. In addition, by combining the auxiliary timer with the Lyapunov method, we obtain the inequality criteria required to achieve quasi-synchronization and derive two different sampling error estimates. Finally, we carefully select Chua’s circuit for relevant numerical simulations to verify the effectiveness of these theoretical results.