Global Mittag-leffler Stability Analysis And Projective Synchronization Of Fractional-order Neural Networks

Fractional order neural networks have been applied in various fields,such as image processing,pattern recognition and so on.At present,the research on its dynamic characteristic has become one of the hottest topics.In this paper,based on fractional order Lyapunov stability theory and linear matrix inequalities(LMIs)technique,we study the issue of the global Mittag-Leffler stability and projective synchronization of the fractional order neural networks.The main work including:1.By designing an appropriate feedback controller and adaptive controller,we investigate global Mittag-Leffler projective synchronization of the fractional order neural networks.By constructing Lyapunov function,the global Mittag-Leffler projective synchronization condition is established in terms of linear matrix inequalities.2.By using fractional Lyapunov-like approach,the global asymptotical stability and convergence in finite time of fractional order differential equations modelling the FNNs dynamics is developed.By applying the proposed convergence in finite time of fractional order system and by designing an appropriate sliding mode and sliding controller,a quantitative estimate of convergence time for nonidentical FNNs global projective synchronization is presented.In addition,a sufficient condition in terms of linear matrix inequalities is given to guarantee global projective synchronization of nonidentical FNNs.3.Based on topological degree theory and Picard successive approximation technique,the existence and uniqueness of equilibrium point and solution are proved respectively.By establishing fractional inequality about integer-order variable upper limit integral and by constructing Lur'e Postnikov Lyapunov function,the global Mittag-Leffler stability of FNNs with piecewise constant argument condition in terms of LMIs is given.