Synchronization of fractional-order linear complex networks.

Area of Science:

• Complex Networks
• Control Theory
• Fractional Calculus

Background:

• Fractional-order complex networks exhibit complex dynamics.
• Network synchronization is crucial for various applications.
• Existing methods often lack generalizability for linear dynamics.

Purpose of the Study:

• To investigate the synchronization problem in fractional-order complex networks with general linear dynamics.
• To develop a novel method for achieving synchronization under connected topology.
• To provide easily solvable conditions for synchronization.

Main Methods:

• Introduced a pseudo-state transformation to convert the synchronization problem.
• Transformed the problem into an equivalent simultaneous stabilization of independent subsystems.
• Utilized nonzero eigenvalues of the Laplacian matrix for characterization.

Main Results:

• Established sufficient conditions for synchronization based on linear matrix inequalities (LMIs).
• Demonstrated that these LMIs can be efficiently solved using convex optimization algorithms.
• Validated the proposed method's effectiveness through three illustrative examples.

Conclusions:

• The proposed pseudo-state transformation method effectively addresses fractional-order complex network synchronization.
• LMIs provide a computationally efficient framework for determining synchronization conditions.
• The findings offer a valuable tool for the analysis and design of synchronized complex systems.