The Passivity of Uncertain Fractional-Order Neural Networks with Time-Varying Delays

Abstract

In this paper, we study the passive problem of uncertain fractional-order neural networks (UFONNs) with time-varying delays. First, we give a sufficient condition for the asymptotic stability of UFONNs with bounded time-varying delays by using the fractional-order Razumikhin theorem. Secondly, according to the above stability criteria and some properties of fractional-order calculus, a delay-dependent condition that can guarantee the passivity of UFONNs with time-varying delays is given in the form of a linear matrix inequality (LMI) that can be reasonably solved in polynomial time using the LMI Control Toolbox. These conditions are not only delay-dependent but also order-dependent, and less conservative than some existing work. Finally, the rationality of the research results is proved by simulation.

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

“…In recently years, the dynamical behavior of fractional-order neural networks (FONN) was widely studied in [22][23][24][25][26][27][28][29][30], especially fractional-order memristive neural networks (FOMNNs) [31][32][33][34][35][36][37][38][39][40][41]. Chen et al investigated Mittag-Leffler synchronization of a FOMNN by using an M-matrix method and set-valued theory in [31].…”

“…One is normbounded uncertainty, and the other is bounded real uncertainty; see [42]. Differently from reference [26,27,36,37,39], a FOMNN with norm-bounded uncertainty is studied for the first time in this article.…”