Open AccessH ∞ observer–controller synthesis approach in low frequency for T–S fuzzy systems
Author(s) -
Xie WenBo,
Han ZhaoKun,
Wu Fen,
Zhu Song
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.2019.0242
Subject(s) - control theory (sociology) , mathematics , robustness (evolution) , eigenvalues and eigenvectors , fuzzy control system , frequency domain , lipschitz continuity , observer (physics) , controller (irrigation) , linear matrix inequality , fuzzy logic , computer science , mathematical optimization , control (management) , physics , quantum mechanics , artificial intelligence , biology , agronomy , mathematical analysis , biochemistry , chemistry , gene
For the output feedback control problem of continuous‐time T–S fuzzy systems with unknown premise variables, an H ∞observer–controller design method in the low‐frequency domain is proposed. First, an observer–controller structure is given, the unknown premise variables are limited by Lipschitz conditions. Then, the system stability conditions are obtained by the negativeness of eigenvalues' real parts. To achieve better control performance of the system in low frequency, the H ∞index for attenuating the unknown low‐frequency disturbance is guaranteed by generalised Kalman–Yakubovich–Popov lemma. Then, the stability and robustness conditions are converted into linear matrix inequality forms, which can be solved directly by a convex optimisation technique. Finally, several simulation examples carried out to show the effectiveness of the proposed method.