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

Abstract

In this paper, we address the asymptotic stability problem for the fractional-order neural networks system with uncertainty based on sampled-data control. First, considering the influence of uncertainty and fractional-order on the system, a new sampled-data control scheme with variable sampling period is designed. According to the input delay approach, the dynamics of the considered fractional-order system is modeled by a delay system. The main purpose of the problem addressed is to design a sampled-data controller, such that the closed-loop fractional-order system can guarantee the asymptotic stability. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are used to derive the stable conditions. The new delay-dependent and order-dependent stability conditions are presented in the form of LMIs. Furthermore, the sampling controller can be obtained to ensure the stability and stabilization of fractional-order system. Finally, a numerical example is given to demonstrate the effectiveness and advantages of the proposed method.

Improved Results on Delay-Dependent and Order-Dependent Criteria of Fractional-Order Neural Networks with Time Delay Based on Sampled-Data Control

“…When δ takes different values of 0.9, 0.92, 0.95, and 0.98, the maximum is 0.426, 0.432, 0.440, and 0.448. The maximum of the reference [22] is 0.12, 0.13, 0.15, and 0.16, which is 255%, 232.3%, 193.3%, and 180% larger than the reference [22], respectively. Additionally, choose δ = 0.98, = 0.448.…”

“…It is obvious that in comparison the results obtained by the method in this article have a greater improvement advantage. Distinctly, when δ takes 0.9, 0.92, 0.95, and 0.98, the maximum is 0.410, 0.415, 0.423, and 0.431, which is an increase of 215.3%, 196.4%, 182%, and 153.5% compared with [26], respectively. Furthermore, taking δ = 0.98, = 0.4315, the corresponding controller gain can be obtained as K =   0.1163 0.0134 0.0066 0.1627 −0.0114 0.0146 0.0484 0.0163 0.0034…”

“…It is obvious that in comparison the results obtained by the method in this article have a greater improvement advantage. Distinctly, when δ takes 0.9, 0.92, 0.95, and 0.98, the maximum is 0.410, 0.415, 0.423, and 0.431, which is an increase of 215.3%, 196.4%, 182%, and 153.5% compared with [26], respectively. Furthermore, taking δ = 0.98, = 0.4315, the corresponding controller gain can be obtained as For the purpose of obtaining simulation results, the initial value is considered as ξ(t 0 ) = [0.9, 0.8, 0.9] T , and through the derived matrix K, the curve of state responses for model (42) is exhibited in Figure 1.…”