Abstract
The robust asymptotical stability and stabilization for a class of fractional-order complex-valued neural networks (FCNNs) with parametric uncertainties and time delay are considered in this paper. It is worth noting that our system combines complex numbers, uncertain parameters, time delay, and fractional orders, which is universal in practical application. Using the theorem of homeomorphism, the sufficient condition of the existence and uniqueness of the equilibrium point for the system is obtained. Then, the sufficient criteria of robust asymptotical stability and stabilization for the addressed models are established, respectively. Finally, we give two numerical examples to verify the feasibility and effectiveness of the theoretical results.
Highlights
Fractional-order calculus, which can be regarded as a generalization of traditional integer-order calculus, has attracted the interest of a lot of researchers in various fields of science and engineering
It mainly depends on the fact that the properties of some actual processes modeled by fractional differential equations will be more accurate or more applicative, such as diffusion processes [1], biological modeling [2], and image processing [3]
When it comes to some actual dynamical systems, it is much better to describe them by fractional-order models rather than the integer-order counterpart, which mainly benefits from the properties of memory and heredity of fractional derivatives
Summary
Fractional-order calculus, which can be regarded as a generalization of traditional integer-order calculus, has attracted the interest of a lot of researchers in various fields of science and engineering. When compared with real-valued fractional-order neural networks, FCNNs are much more complicated because of the state vectors, connection weights, and activation functions of which are all complex values. In [38], by employing the method of the comparison principle, some sufficient conditions were deduced to ensure the robust globally asymptotical synchronization of a class of memristor-based fractional-order complex-valued neural networks with multiple time delays. In [39], authors discussed the robust synchronization of the fractional-order complexvalued neural networks with mixed time-varying delays and impulses by applying the approach of adaptive error feedback control. Inspired by the aforementioned discussion, in this paper, we will study the robust asymptotical stability and stabilization of fractional-order complex-valued delayed neural networks (FCDNNs).
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