Open AccessFeedback stabilisation control design for fractional order non‐linear systems in the lower triangular form
Author(s) -
Zhao Yige,
Wang Yuzhen,
Zhang Xianfu,
Li Haitao
Publication year - 2016
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.2015.0130
Subject(s) - control theory (sociology) , lyapunov function , mathematics , stability theory , state (computer science) , matrix (chemical analysis) , function (biology) , control lyapunov function , lyapunov equation , order (exchange) , fractional calculus , control (management) , computer science , nonlinear system , algorithm , finance , artificial intelligence , economics , physics , materials science , quantum mechanics , evolutionary biology , composite material , biology
Using the Lyapunov function method, this study investigates both state and output feedback stabilisation control design problems for fractional order non‐linear systems in the lower triangular form, and presents a number of new results. First, some new properties for Caputo fractional derivative are presented. Second, by introducing appropriate transformations of coordinates, the feedback stabiliser design problem is converted into the determination of finding some parameters, which can be obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, both state and output feedback stabilisers are explicitly designed to make the closed‐loop system asymptotically stable. The study of an illustrative example shows that the obtained results are effective in designing feedback stabilisers for fractional order non‐linear systems in the lower triangular form.