Exponential Synchronization of Chaotic Lur’e Systems Using Sampled-Data Proportional-Integral Controller and its Application on Chua’s Circuits

This paper uses a proportional-integral (PI) controller to achieve the exponential synchronization of chaotic Lur’e systems under aperiodic sampled-data control. First of all, in order to achieve synchronization of the chaotic Lur’e systems, an aperiodic sampled-data PI controller is constructed. The controller in question incorporates a greater amount of information derived from the sampling sequence than the sampled-data proportional controller. Subsequently, a virtual variable is introduced based on an intermediate variable, thereby constructing a dimension-enhanced synchronization error system. A novel criterion is developed based on virtual variable-related equations for the design of sampled-data PI controllers, with the objective of achieving larger sampling periods and exponential convergence rates in the synchronization process. In the next, a numerical example of neural networks is presented, demonstrating how the developed method in this paper enhances the dynamic performance of the synchronization process in comparison to existing methods. Finally, the developed method is applied to Chua’s circuits, where the real-circuit experiment is made to show its effectiveness.