Global stabilization of fractional-order memristor-based neural networks with incommensurate orders and multiple time-varying delays: a positive-system-based approach

Abstract

This paper addresses global stabilization of fractional-order memristor-based neural networks (FMNNs) with incommensurate orders and multiple time-varying delays (MTDs), where the time delay functions are not necessarily bounded. First, without assuming that time delay functions are bounded, the asymptotical stability condition is given for fractional-order linear positive system with incommensurate orders and MTDs. Then, comparison principle for such a system is established. By virtue of two kinds of vector Lyapunov functions (absolute-value-function-based and square-function-based vector Lyapunov functions), stability condition of fractional-order linear positive system and comparison principle, two stabilization criteria are derived and the equivalence between them is illustrated. In comparison with the reported criterion, the criteria derived in this paper are less conservative, since they allow controller parameters to satisfy weaker algebraic conditions. Lastly, numerical examples are displayed to validate the availability of the controller and correctness of the stabilization criteria.