Research ArticleAdaptive synchronization and parameter identification of chaotic system with unknown parameters and mixed delays based on a special matrix structure

•We propose a new approach to design controller to synchronize and control nonlinear systems with delay.•The approach also can be applied to synchronize and control nonlinear systems with known and unknown parameters.•And with this method, the unknown parameters can be identified.•The approach can also be applied to control and synchronize nonlinear system with mixed delay.

In this paper, we investigate the synchronization and parameter identification of chaotic system with unknown parameters and mixed delays. A new approach is proposed for designing a controller and a update rule of unknown parameters based on a special matrix structure, and the synchronization and the parameter identification are realized under the controller and the update rule. Numerical simulations are carried out to confirm the effectiveness of the approach. A significant advantage is that the process of designing a controller and a update rule become very clear and easy by the proposed approach.