Event‐Triggered Stabilization of a Networked Coevolution Model Coupling Opinion Dynamics With Decision‐Making

This article investigates the stabilization problem for a synchronously updated coevolution model coupling opinion dynamics with decision‐making on a two‐layer network. The synchronous updating mechanism provides a natural description of practical scenarios where individuals may simultaneously revise their opinions and actions after receiving common information, while the stabilization problem reflects the practical need to regulate such coupled evolution through external interventions. However, existing studies on this class of coevolution models mainly focus on asynchronous updating mechanisms and provide limited control‐theoretic results. To fill this gap and address the resulting challenges in stability analysis and controller design, we develop a general hybrid‐system framework by abstracting the considered model into a class of discrete‐time nonlinear hybrid systems with bidirectional coupling between continuous and discrete states. The proposed framework accommodates nonlinear dynamics and general continuous and discrete state spaces beyond the original model. Within this framework, we introduce continuous and discrete control inputs and develop an event‐triggered control scheme (ETCS) to stabilize the system at a desired equilibrium. We subsequently derive sufficient conditions for local uniform asymptotic stabilization under the ETCS. As a byproduct of the main design, we also propose a secondary ETCS and analyze its inter‐execution time. Furthermore, we connect the general theory back to the motivating coevolution model by deriving explicit designs of the ETCS parameters and both continuous and discrete controllers. Finally, numerical simulations of the motivating coevolution model are provided to validate the theoretical results.