Stability Analysis and Synchronization Control of Fractional-Order Inertial Neural Networks With Time-Varying Delay

Abstract

This paper mainly investigates the stability analysis and synchronization control of a fractional-order time-varying delay inertial neural network. Firstly, a time-varying delay inertial neural network model is established, which is easy to implement in engineering applications. Secondly, based on the properties of the Caputo fractional derivative and the proposed lemma, the original inertial system is transferred into conventional system through the proper variable substitution, and a synchronous control strategy for the time varying delay inertial network is then established. In addition, the stability conditions of a class of Caputo fractional-order time-delay inertial neural networks are given. Finally, three simulation examples are given to verify the rationality and effectiveness of the method proposed in this paper.

Anti-periodic Solutions Dynamics for Fractional-order Inertia Cohen-Grossberg Neural Networks

“…Based on Lyapunov functional and new criteria, the authors of [8] studied the asymptotic synchronization and finite time synchronization of fractional-order memristor inertial neural networks with time-varying delays. In reference [9], the author established the stability condition and synchronization control strategy of the Caputo fractional-order inertial neural network with variable delays through means of variable replacement. The author of [10] studied the stability and synchronization of Riemann Liouville fractional-order inertial neural networks with variable delays.…”

Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

“…In contrast to the abundant research results of low-order fractional NNs, there seems to be few reports on the dynamics and control of inertial fractional NNs [39][40][41]. In [39], Gu et al proposed a Lyapunov functional to discuss the stability and synchronization of Riemann-Liouville fractional-order inertial NNs by designing a feedback controller and using a reduced-order method.…”

“…Compared with Riemann-Liouville derivatives, the Caputo fractional derivative has a wider application background. In [41], under the sense of Caputo derivative, the stability and synchronization of fractionalorder inertial NNs with time-varying delay were studied based on the reduced-order technique.…”

“…It is noted that the reduced-order transformation was used in existing results [39][40][41] to reduce the order of the inertial term in the fractional NNs. Correspondingly, the dimension of a couple of the reduced-order systems is double that of the original inertial NNs; this greatly increases the difficulty of theoretical analysis and the complexity of the derived results.…”

“…Correspondingly, the dimension of a couple of the reduced-order systems is double that of the original inertial NNs; this greatly increases the difficulty of theoretical analysis and the complexity of the derived results. On the other hand, in the existing work on the synchronization of fractional inertial NNs [39,41], the controllers were designed for the reduced-order NNs rather than for the original inertial NNs, which imperceptibly increases the difficulty of the implementation of the controllers. Therefore, to reduce the complexity of theoretical analysis and controller design caused by the reduced-order technique, it is valuable to develop a direct method to revisit the dynamics and control of fractional inertial NNs.…”