Designing sampled data controller for time-delayed fractional-order neural networks via a new functional approach

The main focus of this manuscript is vested in the introduction of a new Lyapunov–Krasovskii functional (LKF) for hybrid fractional-order neural networks (FONNs) with Lipschitz non-linearity. The primary originality of this work lies in exploring the possibility of using a new type of functionals similar to looped functional for the stability analysis of hybrid fractional-order systems (FOSs) with delays. Although some work in this direction has been attempted, the formal theory for this concept has not been developed yet. First, a new lemma on establishing asymptotic stability using an arbitrary looped-like LKF and the fractional-order Lyapunov direct method is derived. Using this result, new delay and sampling period dependent stability criteria for the considered FONNs are established in the form of LMIs. Lastly, numerical simulations validate the correctness of the theoretical results proposed in this manuscript.