| Fractional-order calculus as an extension of integral-order calculus,in the process of applying it to the neural network model,it will be more helpful to neuron processing information and has a more accurate description of the dynamic characteristics of the neural network system than the integer-order calculus,because of it has the characteristics of heredity and infinite memory.Hence,the dynamic analysis of the fractional order neural network(FNNs)is a very valuable research topic.The paper is based on the Lyapunov stability theory,the properties of Mittag-Leffler function and the technology of linear matrix inequalities,stability and synchronization of FNNs are investigated in this paper.The main work including:1.The global robust Mittag-Leffler stability analysis for FNNs with parameter uncertainties are preformed.Based on the topological degree theory,the existence and uniqueness of the equilibrium point of the fractional order neural network are proved.By developing the Caputo derivative of integer-order integral function with the variable upper limit and applying Lyapunov functional method,sufficient criterion for global robust Mittag-Leffler stability are given.2.The global Mittag-Leffler stability and finite time stability of FNNs with local Hodler function are discussed.By applying the Lur'e Postnikov type Lyapunov function and the properties of finite time convergence for fractional order systems,a quantitative estimate of the convergence time for FNNs Mittag-Leffler stability with locally Holder activations function is presented,and sufficient conditions for the finite time stability of the FNNs are also given.3.The global Mittag-Leffler synchronization and asymptotically synchronization of FNNs are studied.By designing appropriate linear feedback controller and fractional order adaptive controller,achieving synchronization target and Mittag-Leffler synchronization criterion are addressed in terms of linear matrix inequalities. |
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