带有扰动的适型分数阶时滞系统的稳定分析

Stability analysis of conformable-fractional time-delay systems with disturbances

基于非线性系统Lyapunov稳定理论,在适型分数阶导数意义下,针对带有扰动的导数阶数在开区间(0,1)的分数阶时滞非线性系统,研究其稳定与镇定.首先,基于Lyapunov-Krasovskii泛函思想,给出带有扰动的适型分数阶时滞系统稳定定理.其次,基于TP管控策略,在Filippov解的意义下,给出带有扰动的时滞适型分数阶系统反馈镇定定理.最后,举例说明结果的正确性.

Based on the Lyapunov stability theory of nonlinear systems,the stability and stabilization of conformable fractional-order time-delay nonlinear systems with disturbances where the order of the derivative is in the interval(0,1)are studied.Firstly,based on the Lyapunov-Krasovskii functional theory,stability theorems of conformable fractional-order time-delay nonlinear systems with disturbances are proposed.Secondly,based on TP control strategy and Filippov theory,feedback stabilization theorems for conformable fractional-order time-delay nonlinear systems with disturbances are given.Finally,an example is given to illustrate the correctness of main results.