Stability analysis of fractional-order systems with randomly time-varying parameters
Articles
Dehua Wang
Xi’an Technological University
Xiao-Li Ding
Xi’an Polytechnic University
Juan J. Nieto
Universidade de Santiago de Compostela
https://orcid.org/0000-0001-8202-6578
Published 2021-05-01
https://doi.org/10.15388/namc.2021.26.23053
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Keywords

fractional-order system
randomly time-varying parameters
stability
Lyapunov functional
integral inequalities

How to Cite

Wang D., Ding X.-L. and Nieto J. J. (2021) “Stability analysis of fractional-order systems with randomly time-varying parameters”, Nonlinear Analysis: Modelling and Control, 26(3), pp. 440-460. doi: 10.15388/namc.2021.26.23053.

Abstract

This paper is concerned with the stability of fractional-order systems with randomly timevarying 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.

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