Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: Multiple-parameterization approach

Dong Hwan Lee; Jin Bae Park; Young Hoon Joo

doi:10.1109/TFUZZ.2010.2042720

Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: Multiple-parameterization approach

Dong Hwan Lee, Jin Bae Park, Young Hoon Joo

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Article › peer-review

79 Citations (Scopus)

Abstract

This paper presents the relaxed nonquadratic stabilization conditions of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, we propose a new fuzzy controller and Lyapunov function by generalizing the nonparallel distributed compensation (non-PDC) control law and nonquadratic Lyapunov function, respectively. By exploiting Pólya's theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions, an infinite family of sufficient conditions for the asymptotic stabilizability is derived. These conditions are formulated in the format of linear matrix inequalities (LMIs) and, hence, are numerically tractable via convex programming techniques. Finally, an example is given to illustrate advantages of the proposed method.

Original language	English
Article number	5409609
Pages (from-to)	425-429
Number of pages	5
Journal	IEEE Transactions on Fuzzy Systems
Volume	18
Issue number	2
DOIs	https://doi.org/10.1109/TFUZZ.2010.2042720
Publication status	Published - 2010 Apr

Bibliographical note

Funding Information:
Manuscript received May 21, 2009; revised October 20, 2009; accepted January 18, 2010. First published February 8, 2010; current version published April 2, 2010. This work was supported by Institute of Telecommunications, Multimedia, State-of-charge Information Technology, Yonsei University, a Brain Korea 21 Program, Korea.

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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abstract = "This paper presents the relaxed nonquadratic stabilization conditions of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, we propose a new fuzzy controller and Lyapunov function by generalizing the nonparallel distributed compensation (non-PDC) control law and nonquadratic Lyapunov function, respectively. By exploiting P{\'o}lya's theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions, an infinite family of sufficient conditions for the asymptotic stabilizability is derived. These conditions are formulated in the format of linear matrix inequalities (LMIs) and, hence, are numerically tractable via convex programming techniques. Finally, an example is given to illustrate advantages of the proposed method.",

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note = "Funding Information: Manuscript received May 21, 2009; revised October 20, 2009; accepted January 18, 2010. First published February 8, 2010; current version published April 2, 2010. This work was supported by Institute of Telecommunications, Multimedia, State-of-charge Information Technology, Yonsei University, a Brain Korea 21 Program, Korea.",

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N1 - Funding Information: Manuscript received May 21, 2009; revised October 20, 2009; accepted January 18, 2010. First published February 8, 2010; current version published April 2, 2010. This work was supported by Institute of Telecommunications, Multimedia, State-of-charge Information Technology, Yonsei University, a Brain Korea 21 Program, Korea.

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