Synchronization of chaotic Lur'e systems with time delays using sampled-data control.

Area of Science:

• Control Theory
• Nonlinear Dynamics
• Systems Engineering

Background:

• Chaotic Lur'e systems with time delays present complex dynamics.
• Achieving synchronization in such systems is crucial for various applications.
• Existing methods often yield conservative results.

Purpose of the Study:

• To investigate asymptotical synchronization for identical chaotic Lur'e systems with time delays.
• To develop a less conservative synchronization condition.
• To improve the achievable sampling period for sampled-data control.

Main Methods:

• Employing a sampled-data control method.
• Proposing a new synchronization condition formulated as linear matrix inequalities (LMIs).
• Constructing a novel piecewise differentiable Lyapunov-Krasovskii functional (LKF) that utilizes nonlinear system information.

Main Results:

• The error system is demonstrated to be asymptotically stable using the new LKF.
• The proposed synchronization condition is less conservative than existing methods.
• A longer sampling period is achieved, enhancing control effectiveness.

Conclusions:

• The novel LKF effectively leverages system nonlinearities for improved stability analysis.
• The proposed sampled-data control method offers superior performance and less conservatism.
• Simulations on Chua's circuit validate the effectiveness of the new approach.