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Finite-time mixed outer synchronization of complex networks with coupling time-varying delay
1School of Information Science & Engineering, Northeastern University, Shenyang 110819, People's Republic of China. pinghecn@yahoo.cn
This study introduces finite-time mixed outer synchronization (FMOS) for complex networks with time-varying delays. Novel criteria and a controller ensure synchronization, validated by simulations.
Area of Science:
- Complex Networks
- Nonlinear Dynamics
- Control Theory
Background:
- Generalized synchronization concepts are crucial for understanding complex systems.
- Time-varying delays introduce significant challenges in network synchronization.
- Finite-time control offers faster convergence compared to asymptotic methods.
Purpose of the Study:
- To investigate finite-time mixed outer synchronization (FMOS) in complex networks with coupling time-varying delays.
- To develop novel stability criteria for achieving FMOS.
- To design an effective linear state feedback controller for FMOS.
Main Methods:
- Lyapunov stability theory was employed to derive synchronization criteria.
- Linear matrix inequalities (LMIs) were utilized for stability analysis.
- A linear state feedback controller was designed based on the derived criteria.
Main Results:
- Novel stability criteria for FMOS with coupling time-varying delays were established.
- A feasible linear state feedback controller was designed.
- Numerical simulations demonstrated the effectiveness of the proposed FMOS schemes.
Conclusions:
- The proposed methods effectively achieve finite-time mixed outer synchronization in complex networks.
- The designed controller and criteria provide a robust solution for synchronization problems with time-varying delays.
- The findings advance the control and synchronization of complex dynamical systems.
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