Stability Analysis And Control Of Fractional Networks And Fractional Multi-agent Systems

The dynamic systems described by the fractional differential equation have good memory and inheritance,and can more accurately describe the dynamic behaviors of the systems.Therefore,the research of the fractional dynamic systems have attracted extensive attention all around the world.This paper mainly discusses the stability and synchronization of fractional neural networks and the consensus of fractional multi-agent systems.Its main work is as follows:Firstly,several fractional differential inequalities with respect to convex functions and a novel principle of convergence in finite time for fractional systems are proposed.A class of fractional neural networks with δ-Inverse H?lder activation functions are considered.By using Brouwer’s topology theory and inequality analysis techniques,the existence and uniqueness of the equilibrium point for the neural networks are proved.By means of the Lur’e-Postnikov Lyapunov functional method,sufficient conditions for stability are given.The upper bound of stability in finite time is accurately estimated.Subsequently,a non-fragile controller with two types of gain perturbation is designed for the fractional neural networks with δ-Inverse H?lder activation functions,the conditions of global Mittag-Leffler synchronization and global synchronization in finite time are achieved in terms of linear matrix inequalities.An expression of the upper bound for synchronization in finite time is established.Finally,a class of discontinuous functions subject to nonlinear growth for fractional multi-agent systems are introduced and a nonlinear control protocol,which includes discontinuous factors is designed.Under fractional differential inclusion framework,by means of Lyapunov functional approach and Clarke’s non-smooth analysis technique,the sufficient conditions with respect to the global consensus are achieved.In addition,the setting time is explicitly evaluated for the global leader-following consensus in finite time.