Open AccessConvex Lyapunov functions for stability analysis of fractional order systems
Author(s) -
Chen Weisheng,
Dai Hao,
Song Yanfei,
Zhang Zhengqiang
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.0950
Subject(s) - lyapunov function , mathematics , stability (learning theory) , fractional calculus , order (exchange) , positive definite matrix , regular polygon , lyapunov equation , function (biology) , linear matrix inequality , control theory (sociology) , mathematical optimization , computer science , nonlinear system , control (management) , eigenvalues and eigenvectors , finance , physics , geometry , quantum mechanics , machine learning , artificial intelligence , economics , evolutionary biology , biology
This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag–Leffler stable if there is a convex and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation.