Robust global synchronization of delayed incommensurate fractional-order gene regulatory networks

Abstract

This paper investigates the issue of robust synchronization for delayed incommensurate fractional-order gene regularity networks (IFOGRNs). The common stability analyzing methods for commensurate fractional-order models cannot be used for incommensurate cases. Therefore, the synchronization of the GRNs with incommensurate order models is more challenging than the commensurate ones. This paper employs a novel fractional Lyapunov-based scheme that can be used for incommensurate cases without conversion to a commensurate model. Moreover, this method can analyze the IFOGRNs without linearization, which guarantees global stability. Firstly, some sufficient conditions are proposed for robust controller design when the parameter uncertainties are similar between two such IFOGRNs. It is shown that asymptotic stability is not guaranteed when the parameter uncertainties are not the same. In this paper, a novel adaptive based controller is introduced, which leads to asymptotic stability even for dissimilar parameter uncertainties. Finally, to evaluate the efficiency of the proposed method, some numerical examples are investigated.