Stability analysis of fractional order memristive discontinuous neural networks with partial state control

Abstract

This paper investigates exponential stability of fractional order memristive discontinuous neural networks (FMDNNs). Under the framework of the fractional order Filippov solution and differential inclusion theory, the global existence of the solution for the FMDNNs is studied by a given growth conditions. Based on fractional stability theoryand the properties of the Mittag Leffler function, some new criteria for the stability of FMDNNs are obtained by using effective partial state impulsive control, which only needs to control a small fraction of the states. At every impulsive moment, these states of the trajectory far away from the desired trajectory will be firstly controlled. The relations between stable region and fractional order α, control parameters and control rate are discussed. Finally, a numerical simulation is given to verify the effectiveness of the theoretical analysis.