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A Novel Stability Criteria of a Class Nonlinear Fractional-order HIV-1 System with Multiple Delay

Zhe Zhang*, Jing Zhang, FanYong Cheng, and Feng Liu
International Journal of Control, Automation, and Systems, vol. 17, no. 9, pp.2274-2283, 2019

Abstract : This paper mainly deduces a new stability criteria of the fractional-order HIV-1 system with delay on the basis of Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The Wirtinger inequality is rarely applied to stability analysis of fractional-order system. Nevertheless, this paper extends the general form of the Lyapunov-krasovskii function to a novel fractional expression form by applying definition of Caputo fractional derivative. Via the the integral mean value theorem, fractional-order Lyapunov method and Wirtinger inequality, the novel stability criteria is deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. The simulation results show that the proposed criteria can satisfy different fractional-order operators.In addition, it can not only solve the stability problem of fractional-order HIV-1 system with the constant time delay, but also of the fractional-order HIV-1 system with time-varying time delay. Thus, the new stability criteria has generality and universality. So as to verify our theoretical results, many numerical simulations are provided.

Keyword : Fractional-order, Lyapunov techniques, multiple delay, nonlinear systems, stability analysis.

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