Order-dependent sampling control for state estimation of uncertain fractional-order neural networks system

In this paper, the problem of state estimation for a fractional-order neural networks system with uncertainties is studied by a sampled-data controller. First, considering the convenience of digital field, such as anti-interference, not affected by noise, a novel sampled-data controller is designed for the fractional-order neural network system of uncertainties with changeable sampling time. In the light of the input delay approach, the sampled-data control system of fractional-order is simulated by the delay system. The main purpose of the presented method is to obtain a sampled-data controller gain $K$ to estimate the state of neurons, which can guarantee the asymptotic stability of the closed-loop fractional-order system. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are utilized to derive the stable conditions. Improved delay-dependent and order-dependent stability conditions are given in the form of LMIs. Furthermore, the sampled-data controller can be acquired to promise the stability and stabilization for fractional-order system. Finally, two numerical examples are proposed to demonstrate the effectiveness and advantages of the provided method.