Open AccessGeneralised Kalman–Yakubovich–Popov lemma with its application in finite frequency positive realness control for two‐dimensional continuous‐discrete systems in the Roesser model form
Author(s) -
Wang Lanning,
Wang Weiqun,
Zhang Guangchen,
Chen Weimin
Publication year - 2015
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.2014.0875
Subject(s) - lemma (botany) , mathematics , control theory (sociology) , kalman filter , discrete time and continuous time , bounded function , linear matrix inequality , mathematical analysis , control (management) , computer science , mathematical optimization , statistics , poaceae , artificial intelligence , biology , ecology
This study is concerned with the problem of generalised Kalman–Yakubovich–Popov (GKYP) lemma and its application to two‐dimensional (2D) continuous‐discrete systems described by Roesser model. On the basis of the feature of states in the system, a rectangular finite frequency range is characterised by a linear matrix inequality and then combined with ‐procedure, the GKYP lemma is developed for 2D continuous‐discrete systems in Roesser model. As special cases of this lemma, 2D continuous‐discrete case finite frequency bounded realness and positive realness are investigated as well. Furthermore, the finite frequency 2D positive realness control problem via state‐feedback controllers are considered based on the developed lemma. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.