Open AccessPositive filtering for positive 2D fuzzy systems under ℓ 1 performance
Author(s) -
Wang Li Qun,
Chen Xiaoming,
Shen Jun
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.2018.5211
Subject(s) - control theory (sociology) , bounding overwatch , fuzzy logic , mathematics , positive systems , exponential stability , stability (learning theory) , computer science , linear system , nonlinear system , artificial intelligence , machine learning , mathematical analysis , control (management) , physics , quantum mechanics
In this study, the problem of positive filtering is investigated for positive two‐dimensional (2D) Roesser T–S fuzzy systems under ℓ 1‐induced performance. Error‐bounding positive filters are constructed to estimate the output of positive 2D T–S fuzzy systems. Firstly, a novel characterisation for asymptotic stability of the filtering error system with ℓ 1‐induced performance is derived. Then, based on that characterisation, sufficient conditions are derived to design the required filters expressed by linear programming problems. Finally, the theoretical results are illustrated through a numerical example.