A Fuzzy-PIE Representation of T-S Fuzzy Systems with Delays and Stability Analysis via LPI method

Inspired by the recently proposed Partial Integral Equality(PIE) representation for linear delay systems, this paper proposes a fuzzy-PIE representation for T-S fuzzy systems with delays for the first time. Inspired by the free-weighting matrix technique, this paper introduces the free-weighting Partial Integral (PI) operators. Based on the novel representation and free-weighting PI operators, the stability issue is investigated for the T-S fuzzy systems with delays. The corresponding conditions are given as Linear Partial Inequality (LPI) and can be solved by the MATLAB toolbox PIETOOLS. Compared with the existing results, our method has no need of the bounding technique and a large amount of matrix operation. The numerical examples show the superiority of our method. This paper adds to the expanding field of LPI approach to fuzzy systems with delays.Copyright (C) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)