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Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks
Zhengwen Tu1, Jinde Cao2, Tasawar Hayat3
1Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210996, Jiangsu, China; School of Mathematics and Statistics, and Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Wanzhou 404100, Chongqing, China.
This study investigates global dissipativity in inertial neural networks with time-varying delays and parameter uncertainties. New criteria ensure network stability and identify attractive sets, validated by examples.
Area of Science:
- Control Theory
- Dynamical Systems
- Computational Neuroscience
Background:
- Inertial neural networks (INNs) are crucial for complex computations.
- Time-varying delays and parameter uncertainties pose significant challenges to INN stability analysis.
- Global dissipativity is a key property for ensuring predictable network behavior.
Purpose of the Study:
- To investigate the global dissipativity of inertial neural networks (INNs) with time-varying delays and parameter uncertainties.
- To develop novel criteria for guaranteeing the stability and convergence of these complex systems.
- To provide specific estimations for positive invariant and globally attractive sets within the INNs.
Main Methods:
- Transformation of the original INN system into a first-order differential system.
- Application of matrix measure techniques for stability analysis.
- Utilization of generalized Halanay inequality and matrix-norm inequality.
Main Results:
- Several sufficient criteria for the global dissipativity of INNs were established.
- Specific estimations for positive invariant sets were derived.
- Globally attractive sets for the INNs were precisely determined.
Conclusions:
- The proposed methods effectively ensure the global dissipativity of INNs under considered uncertainties and delays.
- The derived criteria and set estimations offer valuable insights for designing stable and reliable neural network systems.
- Numerical examples confirm the theoretical findings, demonstrating the practical applicability of the results.
