Sampled-data synchronization of chaotic Lur'e systems with time delays

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Chaos Theory

Background:

• Master-slave synchronization of chaotic systems is crucial for secure communications and complex system modeling.
• Time delays and arbitrary sampling in control systems introduce significant challenges to stability analysis and controller design.
• Existing methods often struggle with the conservatism introduced by fixed sampling periods or simplified delay models.

Purpose of the Study:

• To develop a robust sampled-data control strategy for master-slave synchronization of identical chaotic Lur'e systems with time delays.
• To account for arbitrarily varying but bounded sampling periods, enhancing practical applicability.
• To reduce the conservatism typically associated with sampled-data control design for chaotic systems.

Main Methods:

• A novel Lyapunov functional is proposed, designed to be positive definite at sampling instants but not necessarily within intervals.
• Exponential synchronization criteria are derived by analyzing the synchronization error dynamics.
• A linear matrix inequality (LMI) approach is employed for the sampled-data controller design.

Main Results:

• An effective criterion for achieving exponential synchronization under arbitrarily varying sampling is established.
• The proposed Lyapunov functional effectively utilizes sampling information, reducing design conservatism.
• Numerical simulations using Chua's circuit and neural networks validate the controller's effectiveness and improved performance.

Conclusions:

• The developed sampled-data control method provides a less conservative and effective approach for chaotic system synchronization.
• The proposed Lyapunov functional and LMI-based design are suitable for systems with time delays and varying sampling periods.
• The findings contribute to advancing the theory and application of robust control for complex nonlinear systems.