A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method

Abstract In this paper, we propose a new General Stability Criterion (GSC) for the stability analysis of the nonlinear fractional-order systems(FOs) with time delay at all levels based on the deduction of Wirtinger inequality, Integral mean value theorem(IMVT), fractional-order Lyapunov method, and our initiated general Lemma (WILL Deduction Method). This proposed WILL-Deduction method initiates a general lemma to simplify the construction of the GSC. Therefore, the GSC prevails over the previous criteria in that it solves the stability puzzle of all FOs, including all kinds of time-delay with greater flexibility. For all the fractional-order parameters α ∈ 0 , 1 , the GSC is effective. In conclusion, the initially proposed GSC has generality and universality with more efficiency. Finally the numerical simulations have proved the correctness and universality of GSC .