Open AccessLMI relaxations for robust gain‐scheduled control of uncertain linear parameter varying systems
Author(s) -
Sadeghzadeh Arash
Publication year - 2019
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.2018.5373
Subject(s) - control theory (sociology) , inverted pendulum , linear matrix inequality , gain scheduling , mathematics , robust control , scalar (mathematics) , mathematical optimization , controller (irrigation) , robustness (evolution) , upper and lower bounds , linear system , a priori and a posteriori , computer science , control system , control (management) , engineering , nonlinear system , artificial intelligence , mathematical analysis , electrical engineering , philosophy , chemistry , biology , biochemistry , geometry , epistemology , quantum mechanics , agronomy , physics , gene
This study deals with the problem of robust gain‐scheduled dynamic output feedback control for uncertain discrete‐time linear parameter varying systems. The obtained controller guarantees an upper bound on the induced l 2 ‐gain performance of the closed‐loop system. The system matrices are assumed to depend polynomially on both the scheduling and uncertain parameters which are supposed to belong to intervals with a priori known bounds. To formulate the design problem in a linear matrix inequality (LMI) setting, a required auxiliary matrix is initially determined using a necessary condition for finding a gain‐scheduled controller by the proposed method. Then, a robust gain‐scheduled controller is designed by LMI conditions combined with a scalar search using the obtained auxiliary matrix. The method is applied to an inverted pendulum on a cart to illustrate the benefits and applicability of the proposed method.