Finite-Time Stability of Fractional-Order Time-Varying Delays Gene Regulatory Networks with Structured Uncertainties and Controllers

Abstract

In this paper, we investigate a class of fractional-order time-varying delays gene regulatory networks with structured uncertainties and controllers (DFGRNs). Our contributions lie in three aspects: first, a necessary and sufficient condition on the existence of the solution for the DFGRNs is given by using the properties of the Riemann–Liouville fractional derivative and Caputo’s fractional derivative; second, the unique solution of the DFGRNs is proved under given initial function and certain condition; third, some novel sufficient conditions on finite-time stability of the DFGRNs are established by using a generalized Gronwall inequality and norm technique, and some conclusions on the finite-time stability of the DFGRNs with memory state-feedback controllers are reached, and those conditions and conclusions depend on the fractional order of the DFGRNs. One of the most interesting findings is that the “estimated time” of the finite-time stability is indeed related to the structured uncertainties, state-feedback controllers, time delays, and the fractional order of the system.