Research On Global Asymptotically Synchronization Of Discontinuous Neural Networks With Time Delays

Since the neural networks model described by fractional-order can describe the dynamic behaviors of the system more accurately,more and more scholars begin to investigate the dynamic behaviors of the fractional-order neural networks(FNNs).This paper mainly study the synchronization of integer-order and fractional-order neural networks with discontinuous activation functions.The main work are introduced as follows:1.The non-fragile synchronization issue for neural networks(NNs)with discontinuous activation functions,time-varying delays and random feedback gain uncertainties is studied,by designing the non-fragile controller with two types of fluctuations.Under the non-fragile controller,the sufficient synchronization criteria are established in the form of LMIs,by constructing Lyapunov-Krasovskii functions,using differential inclusion theory,non-smooth analysis and multiple integral inequality techniques,and so on.Finally,an example is given to demonstrate the validity of the designed controller and the correctness of the obtained results.2.By using the Lyapunov functional method,the lemmas of fractional differential sys-tems with respect to Mittag-Leffler convergence and convergence in finite time are proposed.By applying the fractional differential inclusion theory,non-smooth analysis and the two pro-posed lemmas,the Mittag-Leffler synchronization and the synchronization in finite time of discontinuous FNNs with delay are investigated,and the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated.3.Under the designed non-fragile controller,we discussed the global robust Mittag-Leffler synchronization issue of discontinuous FNNs with uncertain parameters.By propos-ing a new inequality,which is concerned with the fractional derivative of the variable upper limit integral for the non-smooth integrable functional,and constructing Lur'e Postnikov Lyapunov Funtionals,applying Lyapunov stability theory and a series of inequality tech-niques,the sufficient synchronization conditions are addressed in terms of LMIs.