Master–Slave Finite-Time Synchronization of Chaotic Fractional-Order Neural Networks under Hybrid Sampled-Data Control: An LMI Approach

Abstract In this paper, a hybrid controller with a sampled data control is investigated to achieve finite-time master–slave synchronization of delayed fractional-order neural networks (DFONNs). A Lyapunov-Krasovskii functional is constructed to obtain the sufficient conditions that incorporate delay information. For the first time, the asymptotic stability of the error system is guaranteed in a finite-time using the inequality technique and a sampled-data hybrid controller. The obtained conditions are expressed via linear matrix inequality. Notably, the proposed approach outperforms existing methods, demonstrating improved results in a comparative analysis. An explicit formula is utilized to calculate the settling time, which is significantly influenced by the fractional order $$0&lt;\beta \le 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>β</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . The superior performance of the proposed control method is evident, showcasing its effectiveness through numerical simulations and addressing the synchronization problem in DFONNs.