Lyapunov Functional Approach to Stability Analysis of Riemann‐Liouville Fractional Neural Networks with Time‐Varying Delays

Abstract

This paper is concerned with the globally asymptotic stability of the Riemann‐Liouville fractional‐order neural networks with time‐varying delays. The Lyapunov functional approach to stability analysis for nonlinear fractional‐order functional differential equations is discussed. By constructing an appropriate Lyapunov functional associated with the Riemann‐Liouville fractional integral and derivative, the asymptotic stability criteria of fractional‐order neural networks with time‐varying delays and constant delays are derived. The advantage of our proposed method is that one may directly calculate the first‐order derivative of the Lyapunov functional. Two numerical examples are also presented to illustrate the validity and feasibility of the theoretical results. With the increasing of the order of fractional derivatives, the state trajectories of neural networks show that the speeds of converging toward zero solution are faster and faster.

Stabilization of switched neural networks with time‐varying delay via bumpless transfer control

“…respectively. According to the stability or stabilization results presented in [7,25,26,29], the above control gains can also guarantee that the switched neural networks is exponential stabilizable under the classical switching feedback controller (2). Figures 2 and 3 show that the stable time response curves of this neural network with the feedback controller (3) and the curves of control input of the controller (3), respectively.…”

“…Figures 2 and 3 show that the stable time response curves of this neural network with the feedback controller (3) and the curves of control input of the controller (3), respectively. In order to give the comparison results between bumpless transfer control and the non-bumpless transfer control [7,26,29], we have also plotted the time response curves of this switched neural network with the controller (2) and the curves of control input of the controller (2). As shown in Figure 2, we know that this switched neural network can be stabilized by both the controller (2) and the controller (3).…”

On the PC $\mathcal{PC}$ -mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

“…One of the most fundamental definitions of fractional integral of arbitrary order is the Riemann-Liouville fractional derivative operator which will be defined further on. This operator has novel applications in the modeling and study the neural networks [50], electrical conductivity and temperature control [44], etc., see also [8,16,40,45].…”

Discrete Fractional‐Order BAM Neural Networks with Leakage Delay: Existence and Stability Results

“…Fractional‐order operators which provide better representation for processes involving infinite memory have been successfully integrated into neural networks. Recent years have witnessed the appearance of tremendous number of papers studying the dynamical behavior of various types of fractional‐order neural networks . Particularly, the stability of fractional neural networks with delays has been the object of much research in the last years.…”