Exponential H∞ synchronization and state estimation for chaotic systems via a unified model

Area of Science:

• Control Theory
• Nonlinear Dynamics
• Chaos Theory

Background:

• Chaotic systems exhibit complex dynamics.
• Synchronization and state estimation are crucial for controlling chaotic systems.
• Existing methods often lack a unified approach for diverse chaotic systems.

Purpose of the Study:

• To develop a unified framework for H∞ synchronization and state estimation of chaotic systems.
• To design robust controllers and estimators minimizing external disturbances and noise.
• To demonstrate the applicability to various chaotic systems like neural networks and Chua's circuits.

Main Methods:

• Utilizing a unified model combining linear dynamics and nonlinear operators.
• Applying H∞ performance analysis via linear matrix inequality (LMI).
• Solving eigenvalue problems for controller and filter parameter determination.

Main Results:

• Novel state feedback controllers guaranteeing exponential synchronization stability.
• State estimators ensuring exponential stability of estimation error dynamics.
• Demonstrated reduction of disturbance and noise effects to H∞ norm constraints.

Conclusions:

• The unified model and H∞ approach provide a general solution for chaotic system synchronization and state estimation.
• The proposed methods are effective for a wide range of chaotic systems.
• Numerical examples validate the practical utility of the developed H∞ synchronization and state estimation conditions.