Fractional-Order Switched Neural Networks via Saturated Control Design and Impulsive Approach: Finite-Time Case

This paper investigates the finite-time stabilization of fractional-order impulsive switched neural networks subject to actuator saturation. Such systems combine memory-dependent fractional dynamics, mode switching, impulsive updates, and bounded control inputs—features that frequently coexist in practical networks but have not previously been treated together. To address this, an impulsive control framework is developed in which the actuator saturation is handled through a convex-hull representation. Using Lyapunov stability theory, the average dwell time approach, and the Gronwall–Bellman inequality, sufficient conditions are derived to guarantee finite-time stability of the closed-loop system, and the controller gains are obtained by solving a set of linear matrix inequalities via the MATLAB (2019a) LMI toolbox. The effectiveness of the proposed strategy is validated on two-dimensional and three-dimensional numerical examples: in both cases, the synchronization error is driven below the prescribed finite-time bound (c2=2.5 and c2=3.5, respectively) within the finite-time horizon, while the state remains inside the admissible region despite the saturation constraint. A sensitivity analysis across fractional orders α∈{0.85,0.90,0.95,0.99} further confirms that finite-time stability is preserved throughout, with faster convergence at smaller α.