Synchronization In Finite Time Control For Fractional-order Discontinuous Complex Networks

The dynamic system characterized by fractional differential operator has good heritability and memory,which attracts the attention of many researchers.In particular,the study for fractional-order complex network dynamic behaviour has become a hot topic in the field of mathematics and information science.In this paper,the synchronization in finite time for fractional-order discontinuous complex network is studied.The main results obtained of this paper are as follows:Firstly,for fractional-order complex networks with discontinuous dynamic nodes,when the coupling connection weight matrix is time-varying and satisfies certain adaptive conditions,by taking advantage of the non-smooth analysis method,Lyapunov stability theory and Laplace transform technique,the global Mittag-Leffler synchronization conditions are obtained in the form of linear matrix inequality(LMIs).When the coupling connection is a constant matrix and the discontinuous nodes satisfy the nonlinear local H?lder growth,the conditions of global synchronization in finite time are established in terms of LMIs by using the Lur’e postnikov-type Lyapunov functional under the designed feedback controller.Furthermore,the upper bound of settling time is accurately estimated.Secondly,for a class of complex fractional-order discontinuous delay networks with quadratic polynomial nonlinear growth,the global robust synchronization in finite time conditions are given by using the established fractional-order differential inequality under the designed discontinuous feedback controller,and the upper bound of settling time estimation formula is given.Finally,for fractional-order discontinuous complex network with multi-weights and uncertain coupling,under the Filippov Differential inclusion framework,using multiple Lyapunov functionals and the average dwell time method,under the designed controller with switching gains,the global robust non-fragile synchronization in finite time conditions are given in terms of LMIs.Furthermore,the upper bound of the average dwell time is explicitly evaluated.