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Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter
Qiankun Song1, Qinqin Yu2, Zhenjiang Zhao3
1Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China.
Summary
This study investigates the stability of complex-valued neural networks with uncertain parameters. A new criterion ensures network boundedness and robust stability of the equilibrium point, verifiable with MATLAB.
Area of Science:
- Complex-valued neural networks
- Control theory
- Robust stability analysis
Background:
- Neural networks are crucial in complex systems.
- Parameter uncertainties and time delays pose stability challenges.
- Robustness analysis is vital for reliable network performance.
Purpose of the Study:
- Investigate boundedness and robust stability of delayed complex-valued neural networks with interval parameter uncertainties.
- Develop a sufficient condition for network boundedness and equilibrium point stability.
- Provide a computable criterion for practical applications.
Main Methods:
- Utilized Homomorphic mapping theorem, Lyapunov method, and inequality techniques.
- Formulated a complex-valued Linear Matrix Inequality (LMI) for stability analysis.
- Employed YALMIP with the SDPT3 solver in MATLAB for numerical computation.
Main Results:
- Derived a sufficient condition guaranteeing network boundedness.
- Established the existence, uniqueness, and global robust stability of the equilibrium point.
- Presented a complex-valued LMI criterion for robust stability.
Conclusions:
- The derived criterion ensures the robust stability of uncertain complex-valued neural networks.
- The LMI-based approach is numerically tractable using standard software.
- The study offers a valuable tool for designing and analyzing complex-valued neural networks.
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