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Title: Stability analysis and stabilization of polynomial fuzzy-model-based control systems using piecewise linear membership functions
Authors: Lam, HK
Narimani, M
Leung, FHF 
Keywords: Lyapunov methods
Closed loop systems
Control system analysis
Control system synthesis
Fuzzy control
Piecewise linear techniques
Polynomial approximation
Issue Date: 2010
Publisher: IEEE
Source: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), 18-23 July 2010, Barcelona, p. 1-8 How to cite?
Abstract: This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB control system is not required that the polynomial fuzzy controller shares the same premises membership functions as those of the polynomial fuzzy model. Piecewise linear membership functions are employed to approximate the membership functions of the polynomial fuzzy model and polynomial fuzzy controller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear membership functions offer a nice property that the grades of membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear membership functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear membership functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB control systems with the specified piecewise linear membership functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
ISBN: 978-1-4244-6919-2
ISSN: 1098-7584
DOI: 10.1109/FUZZY.2010.5584205
Appears in Collections:Conference Paper

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