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Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method
- Source :
- IEEE Access, Vol 9, Pp 124132-124141 (2021)
- Publication Year :
- 2021
- Publisher :
- IEEE, 2021.
-
Abstract
- At present, the theory and application of fractional-order neural networks remain in the exploratory stage. We study the asymptotic stability of fractional-order neural networks with Riemann-Liouville (R-L) derivatives. For non-delayed and delayed systems, we propose an asymptotic stability criterion based on the combination of the Lyapunov method and linear matrix inequality (LMI) method. The highlights include the following: (1) for fractional-order neural networks with time delay, the existence and uniqueness of solutions are proven by using matrix analysis theory and contraction mapping theorem, and (2) based on the unique solution, a suitable Lyapunov functional is constructed. Based on the inequality theorem and LMI method, two sets of asymptotic stability criteria for fractional-order neural networks are proven, which avoids the difficulty of solving the fractional derivative by the Leibniz law. Finally, the results are verified using numerical simulations.
Details
- Language :
- English
- ISSN :
- 21693536
- Volume :
- 9
- Database :
- Directory of Open Access Journals
- Journal :
- IEEE Access
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.fc9ed664c2049c5b5eeb39bec75e47d
- Document Type :
- article
- Full Text :
- https://doi.org/10.1109/ACCESS.2021.3110764