Open AccessStability analysis of discrete‐time positive polynomial‐fuzzy‐model‐based control systems through fuzzy co‐positive Lyapunov function with bounded control
Author(s) -
Li Xiaomiao,
Mehran Kamyar,
Lam Hak Keung,
Xiao Bo,
Bao Zhiyong
Publication year - 2020
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.2019.0133
Subject(s) - mathematics , lyapunov function , control theory (sociology) , lyapunov redesign , polynomial , fuzzy control system , bounded function , lyapunov equation , fuzzy logic , lyapunov exponent , fuzzy number , mathematical optimization , fuzzy set , nonlinear system , computer science , mathematical analysis , control (management) , artificial intelligence , chaotic , physics , quantum mechanics
This study employs a novel fuzzy co‐positive Lyapunov function to investigate the stability of discrete‐time polynomial‐fuzzy‐model‐based control systems under positivity constraint. The fuzzy co‐positive Lyapunov function consists of a number of local sub‐Lyapunov function candidates which includes the positivity property of a non‐linear system and the contribution of each sub‐Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed‐loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and positivity conditions, in which all are formulated in the form of sum‐of‐squares conditions. A numerical example is given to validate the proposed approach.