Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses

Abstract

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.

Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior

“…We will use the following definition for Mittag-Leffler stability of the state of the model (5) [ 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 ].…”

“…For fractional-order models the concept of Mittag-Leffler stability, introduced in Reference [ 45 ], is adapted as a generalization of the exponential stability notion in integer-order systems [ 46 , 47 , 48 ]. Very recently, the Mittag-Leffler notion has been also applied to fractional-order control problems [ 49 , 50 , 51 ], including impulsive controls in neural network systems [ 47 , 52 , 53 , 54 ]. The Mittag-Leffler stability and impulsive control strategies have not been investigated for fractional generalizations of the cooperative Lotka-Volterra model (1) which are important and challenging problems and one of the main goals of the present research.…”

Finite-Time Synchronization and Passivity of Multiple Delayed Coupled Neural Networks via Impulsive Control

“…Remark 6: It should be noted that parameter uncertainty may occur frequently in neural network models due to modeling errors, external disturbances, and parameter fluctuations [42], [43]. As far as we know, there are no reports on the robust FTP and FTS of MDCNNs via impulsive control.…”

Observer Design for Fractional-Order Chaotic Neural Networks With Unknown Parameters

“…In [13], by using a kind of new fractional differential inequalities, synchronisation of FONNs in the presence of time-varying delays was addressed. In [14], some sufficient conditions about the stability of impulsive FONNs with and without uncertain parameters were established, and robust generalized M-L synchronization of FONNs with discontinuous activation and impulses by using these conditions were also investigated. However, in above literature, a key assumption is that the states of the FONNs are available.…”