A novel stability criterion of the time-lag fractional-order gene regulatory network system for stability analysis

This paper presents a novel stability criterion of the time-lag fractional-order gene regulation network system(FGRNs) for stability analysis by means of Jensen inequality, Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The two inequalities are often seen, applied to the stability analysis of integer-order gene regulation network system, but rarely to that the FGRNs. However, this paper extends the general form of the Lyapunov-krasovskii function to a new fractional expression form by applying the definition of Caputo fractional derivative to the FGRNs. From the fractional-order Lyapunov method, the integral mean value theorem and the two inequalities, the novel stability criterion are deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. Experiments show that the proposed criterion can satisfy all fractional-order operators from 0 to 1. It can not only solve the stability problem of the constant time-lag FGRNs, but also that of the time-varying time-lag FGRNs. Consequently, the novel stability criterion has generality and universality, which has been verified by numerical simulations for its effectiveness and generality.