Abstract
The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way. Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
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Project supported by the National Natural Science Foundation of China (No. 60504024), and the Research Project of Zhejiang Provincial Education Department (No. 20050905), China
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Zhang, Jh., Zhang, Sl. & Liu, Mq. Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks. J. Zhejiang Univ. - Sci. A 8, 1912–1920 (2007). https://doi.org/10.1631/jzus.2007.A1912
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DOI: https://doi.org/10.1631/jzus.2007.A1912
Key words
- Standard neural network model (SNNM)
- Robust exponential stability
- Recurrent neural networks (RNNs)
- Discrete-time
- Time-delay system
- Linear matrix inequality (LMI)