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Stability Analysis and Estimation of Domain of Attraction for Positive Polynomial Fuzzy Systems with Input Saturation

Research output: Contribution to journalArticle

Meng Han, Hak Keung Lam, Fucai Liu, Likui Wang, Yinggan Tang

Original languageEnglish
Article number8731708
Pages (from-to)1723-1736
Number of pages14
JournalIEEE Transactions on Fuzzy Systems
Volume28
Issue number8
DOIs
PublishedAug 2020

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Abstract

In this paper, the stability and positivity of positive polynomial fuzzy model based (PPFMB) control system are investigated, in which the positive polynomial fuzzy model and positive polynomial fuzzy controller are allowed to have different premise membership functions from each other. These mismatched premise membership functions can increase the flexibility of controller design; however, it will lead to the conservative results when the stability is analyzed based on the Lyapunov stability theory. To relax the positivity/stability conditions, the improved Taylor-series-membership-functions-dependent (ITSMFD) method is introduced by introducing the sample points information of Taylor-series approximate membership functions, local error information and boundary information of substate space of premise variables into the stability/positivity conditions. Meanwhile, the ITSMFD method is extended to the PPFMB control system with input saturation to relax the estimation of domain of attraction. Finally, simulation examples are presented to verify the feasibility of this method.

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