Approaches to extended non-quadratic stability and stabilization conditions for discrete-time TakagiSugeno fuzzy systems

Dong Hwan Lee; Jin Bae Park; Young Hoon Joo

doi:10.1016/j.automatica.2010.10.029

Approaches to extended non-quadratic stability and stabilization conditions for discrete-time TakagiSugeno fuzzy systems

Dong Hwan Lee, Jin Bae Park, Young Hoon Joo

Department of Electrical and Electronic Engineering

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

68 Citations (Scopus)

Abstract

This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time TakagiSugeno (TS) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the l-step-past (l≥0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.

Original language	English
Pages (from-to)	534-538
Number of pages	5
Journal	Automatica
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/j.automatica.2010.10.029
Publication status	Published - 2011 Mar 3

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.automatica.2010.10.029

Cite this

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title = "Approaches to extended non-quadratic stability and stabilization conditions for discrete-time TakagiSugeno fuzzy systems",

abstract = "This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time TakagiSugeno (TS) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the l-step-past (l≥0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.",

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AU - Lee, Dong Hwan

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AU - Joo, Young Hoon

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Y1 - 2011/3/3

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AB - This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time TakagiSugeno (TS) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the l-step-past (l≥0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.

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Approaches to extended non-quadratic stability and stabilization conditions for discrete-time TakagiSugeno fuzzy systems

Abstract

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