Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method

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.

Automated summary

This study explores the theory and application of fractional-order neural networks, focusing on the asymptotic stability with Riemann-Liouville derivatives. The proposed stability criteria are based on Lyapunov and LMI methods, showcasing the uniqueness of solutions using matrix analysis and contraction mapping theory for delayed systems. The results provide two sets of asymptotic stability criteria for fractional-order neural networks, verified through numerical simulations.