Stability analysis of fractional-order systems with randomly time-varying parameters

被引：1

作者：

Wang, Dehua ^{[1
,2
]}

Ding, Xiao-Li ^{[3
]}

Nieto, Juan J. ^{[4
]}

机构：

[1] Xian Technol Univ, Sch Sci, Xian 710021, Shaanxi, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610054, Sichuan, Peoples R China

[3] Xian Polytech Univ, Dept Math, Xian 710048, Shaanxi, Peoples R China

[4] Univ Santiago de Compostela, Inst Matemat, Dept Estatist Anal Matemat & Optimizac, Santiago De Compostela 15782, Spain

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2021年 / 26卷 / 03期

关键词：

fractional-order system; randomly time-varying parameters; stability; Lyapunov functional; integral inequalities; STOCHASTIC DIFFERENTIAL-EQUATIONS; MITTAG-LEFFLER STABILITY; RANDOM-WALKS; INCLUSIONS; DIFFUSION; DRIVEN;

D O I：

10.15388/namc.2021.26.23053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the stability of fractional-order systems with randomly time-varying parameters. Two approaches are provided to check the stability of such systems in mean sense. The first approach is based on suitable Lyapunov functionals to assess the stability, which is of vital importance in the theory of stability. By an example one finds that the stability conditions obtained by the first approach can be tabulated for some special cases. For some complicated linear and nonlinear systems, the stability conditions present computational difficulties. The second alternative approach is based on integral inequalities and ingenious mathematical method. Finally, we also give two examples to demonstrate the feasibility and advantage of the second approach. Compared with the stability conditions obtained by the first approach, the stability conditions obtained by the second one are easily verified by simple computation rather than complicated functional construction. The derived criteria improve the existing related results.

引用

页码：440 / 460

页数：21

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