Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback inte...

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Main Authors: Zhixiong Zhong, Guanghui Sun, Hamid Reza Karimi, Jianbin Qiu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/913234
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spelling doaj-3d12ad0fecbc4c67905cbe1c37e79a472020-11-24T22:52:43ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/913234913234Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output ApproachZhixiong Zhong0Guanghui Sun1Hamid Reza Karimi2Jianbin Qiu3Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaSpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaFaculty of Engineering and Science, University of Agder, N-4898 Grimstad, NorwaySpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaThe stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.http://dx.doi.org/10.1155/2013/913234
collection DOAJ
language English
format Article
sources DOAJ
author Zhixiong Zhong
Guanghui Sun
Hamid Reza Karimi
Jianbin Qiu
spellingShingle Zhixiong Zhong
Guanghui Sun
Hamid Reza Karimi
Jianbin Qiu
Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
Mathematical Problems in Engineering
author_facet Zhixiong Zhong
Guanghui Sun
Hamid Reza Karimi
Jianbin Qiu
author_sort Zhixiong Zhong
title Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
title_short Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
title_full Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
title_fullStr Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
title_full_unstemmed Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach
title_sort stability analysis and stabilization of t-s fuzzy delta operator systems with time-varying delay via an input-output approach
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.
url http://dx.doi.org/10.1155/2013/913234
work_keys_str_mv AT zhixiongzhong stabilityanalysisandstabilizationoftsfuzzydeltaoperatorsystemswithtimevaryingdelayviaaninputoutputapproach
AT guanghuisun stabilityanalysisandstabilizationoftsfuzzydeltaoperatorsystemswithtimevaryingdelayviaaninputoutputapproach
AT hamidrezakarimi stabilityanalysisandstabilizationoftsfuzzydeltaoperatorsystemswithtimevaryingdelayviaaninputoutputapproach
AT jianbinqiu stabilityanalysisandstabilizationoftsfuzzydeltaoperatorsystemswithtimevaryingdelayviaaninputoutputapproach
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