Open AccessStability of fractional‐order nonlinear systems by Lyapunov direct method
Author(s) -
Tuan Hoang T.,
Trinh Hieu
Publication year - 2018
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.2018.5233
Subject(s) - fractional calculus , mathematics , lyapunov function , nonlinear system , order (exchange) , lyapunov redesign , stability (learning theory) , lyapunov exponent , control theory (sociology) , lyapunov equation , computer science , control (management) , physics , finance , quantum mechanics , machine learning , artificial intelligence , economics
In this study, by using a characterisation of functions having a fractional derivative, the authors propose a rigorous fractional Lyapunov function candidate method to analyse the stability of fractional‐order nonlinear systems. First, they prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption of the existence of the derivative of pseudo‐states. Second, they establish fractional Lyapunov functions to fractional‐order systems without the assumption of the global existence of solutions. Their theorems fill the gaps and strengthen results in some existing papers.