Premium
Approaches to robust ℋ︁ ∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties
Author(s) -
Qiu Jianbin,
Feng Gang,
Gao Huijun
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1627
Subject(s) - control theory (sociology) , mathematics , parameterized complexity , parametric statistics , bounded function , discrete time and continuous time , norm (philosophy) , exponential stability , lyapunov function , linear matrix inequality , robust control , controller (irrigation) , computer science , mathematical optimization , control system , nonlinear system , algorithm , control (management) , engineering , mathematical analysis , statistics , physics , electrical engineering , quantum mechanics , artificial intelligence , political science , law , agronomy , biology
This paper investigates the problem of robust ℋ ∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ℋ ∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.