Global Mittag-Leffler Stabilization Of Fractional-order Complex-valued Memristive Neural Networks

As an extension of the real-valued neural networks,complex-valued neural net-works have complex-valued states,synaptic weights,and the activation functions.Compared with the real-valued systems,complex-valued system have more excellent and complicated properties,it can solve many problems that real-valued systems diffi-cult to solve.Meanwhile,compared with the classical integer order models,fractional-order derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes.This paper presents the the-oretical results about global Mittag-Leffler stabilization for a class of fractional-order complex-valued memristive neural networks with the designed two types of control rules.By utilizing the set-valued maps,a generalized fractional derivative inequality as well as fractional-order differential inclusions,several stabilization criteria for global Mittag-Leffler stabilization of fractional-order complex-valued memristive neural net-works are established.The specific works of this dissertation are as follows:Chapter 1 gives the research background and significance of fractional-order complex-valued memristive neural networks,including the introduction of memris-tor,the research status of fractional-order complex-valued memristive neural networks.Then some revelent definitions and lemmas are given.Finally,some necessary prelim-inaries and the main contents of this dissertation are also introduced at the end of this chapter.Chapter 2 analyzes the global Mittag-Leffler stabilization of fractional-order complex-valued memristive neural networks under the control of state feedback,by utilizing the set-valued maps,a generalized fractional derivative inequality as well as fractional-order differential inclusions,several stabilization criteria for global Mittag-Leffler stabilization of fractional-order complex-valued memristive neural networks are established.Chapter 3 discusses the global Mittag-Leffler stabilization of fractional-order complex-valued memristive neural networks when the state variables are not measur-able,we design the stabilization control via output feedback,then utilizing the set-valued maps,fractional-order differential inclusions and structuring different Lyapunov function to analyzes the global Mittag-Leffler stabilization.Finally,Chapter 4 summarizes the research conclusions and points out the prob-lems to be further research in the future.