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Robust Stability Analysis of Delayed Stochastic Neural Networks via Wirtinger-Based Integral Inequality
1Department of Applied Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, India 602 117 sureshsiththan@gmail.com.
Neural Computation
|November 30, 2020
Summary
This study presents new methods for analyzing the stability of uncertain stochastic neural networks with time delays. The research provides conditions to ensure the global, asymptotic stability of these complex systems.
Area of Science:
- Control Systems Engineering
- Computational Neuroscience
- Applied Mathematics
Background:
- Stochastic Neural Networks (SNNs) are crucial in modeling complex systems.
- Time delays and parameter uncertainties introduce significant challenges in SNN stability analysis.
- Ensuring the stability of SNNs is vital for reliable system performance.
Purpose of the Study:
- To develop novel stability criteria for uncertain stochastic neural networks with time delays.
- To address the complexities introduced by parameter uncertainties and time-varying delays.
- To provide a robust framework for analyzing the global, asymptotic stability of SNNs.
Main Methods:
- Construction of a suitable Lyapunov-Krasovskii functional (LKF).
- Application of Wirtinger inequalities for integral inequality estimation.
- Derivation of delay-dependent stability conditions using linear matrix inequalities (LMIs).
- Analysis of parameter uncertainties under norm-bounded conditions.
Main Results:
- Novel delay-dependent stochastic stability conditions for uncertain SNNs are derived.
- The derived conditions guarantee global, asymptotic stability of the network states.
- The effectiveness of the proposed criteria is validated through numerical examples.
Conclusions:
- The proposed LMI-based approach effectively ensures the stability of uncertain SNNs with time delays.
- The methodology offers a significant advancement in the stability analysis of complex neural network models.
- The findings have implications for the design and application of robust SNNs in various fields.
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