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Stability analysis for fractional‐order neural networks with time‐varying delay
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SummaryThis paper focuses on the stability analysis for fractional‐order neural networks with time‐varying delay. A novel Lyapunov's asymptotic stability determination theorem is proved, which can be used for fractional‐order systems directly. Different from the classical Lyapunov stability theorem, constraint condition on the derivative of Lyapunov function is revised as an uniformly continuous class‐K function in the fractional‐order case. Based on this novel Lyapunov stability theorem and free weight matrix method, a new sufficient condition on Lyapunov asymptotic stability of fractional‐order Hopfield neural networks is derived by constructing a suitable Lyapunov function. Moreover, two numerical examples are provided to illustrate the effectiveness of these criteria.
Title: Stability analysis for fractional‐order neural networks with time‐varying delay
Description:
SummaryThis paper focuses on the stability analysis for fractional‐order neural networks with time‐varying delay.
A novel Lyapunov's asymptotic stability determination theorem is proved, which can be used for fractional‐order systems directly.
Different from the classical Lyapunov stability theorem, constraint condition on the derivative of Lyapunov function is revised as an uniformly continuous class‐K function in the fractional‐order case.
Based on this novel Lyapunov stability theorem and free weight matrix method, a new sufficient condition on Lyapunov asymptotic stability of fractional‐order Hopfield neural networks is derived by constructing a suitable Lyapunov function.
Moreover, two numerical examples are provided to illustrate the effectiveness of these criteria.
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