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Non-fragile output-feedback synchronization for delayed discrete-time complex-valued neural networks with randomly
1Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram 624 302, Tamil Nadu, India.
Summary
This study establishes an exponential synchronization criterion for discrete-time complex-valued neural networks (CVNNs) with time-varying delays. New methods ensure stability and control, offering less restrictive conditions for synchronization.
Area of Science:
- Control Theory
- Neural Networks
- Complex Systems
Background:
- Discrete-time complex-valued neural networks (CVNNs) face synchronization challenges due to time-varying delays and parameter uncertainties.
- Output-feedback controllers can introduce fluctuations affecting network dynamics and stability.
Purpose of the Study:
- To establish a novel exponential synchronization criterion for discrete-time CVNNs with time-varying delays.
- To develop an effective output-feedback controller to manage parameter uncertainties and network fluctuations.
- To overcome limitations of existing synchronization methods for complex-valued neural networks.
Main Methods:
- Extension of Jensen's weighted summation inequalities (WSIs) and extended reciprocal convex matrix inequality (ERCMI) to the complex field.
- Construction of a Lyapunov-Krasovskii functional (LKF) with augmented vectors for improved delay-dependent analysis.
- Linearization of quadratic summation terms using developed complex-valued inequalities.
Main Results:
- A less restrictive exponential synchronization criterion for discrete-time CVNNs is proposed.
- The method requires fewer decision variables compared to existing inequalities.
- An output-feedback control gain is designed by solving complex-valued linear matrix inequalities (LMIs).
Conclusions:
- The proposed criterion effectively achieves exponential synchronization for discrete-time CVNNs with time-varying delays and uncertainties.
- The developed methods provide a more robust and efficient approach to synchronization problems in complex neural networks.
- Numerical simulations confirm the validity and effectiveness of the established results.
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