A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays

A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays

This paper investigates the ℓ2-ℓ∞ filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition on ℓ2-ℓ∞-disturbance attenuation is presented, in which both stab...

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Main Authors: Xiaoyu Zhang, Cheng Gong, Zhen Zeng
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/298268
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spelling doaj-0e512f8bce0a410ba6404bff999896d42020-11-24T21:38:53ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/298268298268A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying DelaysXiaoyu Zhang0Cheng Gong1Zhen Zeng2College of Automation, Harbin Engineering University, Harbin 150001, ChinaCollege of Nuclear Science and Technology, Harbin Engineering University, Harbin 150001, ChinaCollege of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, ChinaThis paper investigates the ℓ2-ℓ∞ filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition on ℓ2-ℓ∞-disturbance attenuation is presented, in which both stability and prescribed ℓ2-ℓ∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependent ℓ2-ℓ∞ filter design schemes for T-S fuzzy multiple time-varying delays systems are developed in terms of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.http://dx.doi.org/10.1155/2013/298268
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoyu Zhang
Cheng Gong
Zhen Zeng
spellingShingle Xiaoyu Zhang
Cheng Gong
Zhen Zeng
A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
Mathematical Problems in Engineering
author_facet Xiaoyu Zhang
Cheng Gong
Zhen Zeng
author_sort Xiaoyu Zhang
title A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
title_short A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
title_full A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
title_fullStr A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
title_full_unstemmed A Novel Approach to ℓ2-ℓ∞ Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays
title_sort novel approach to ℓ2-ℓ∞ filter design for t-s fuzzy systems with multiple time-varying delays
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description This paper investigates the ℓ2-ℓ∞ filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition on ℓ2-ℓ∞-disturbance attenuation is presented, in which both stability and prescribed ℓ2-ℓ∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependent ℓ2-ℓ∞ filter design schemes for T-S fuzzy multiple time-varying delays systems are developed in terms of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.
url http://dx.doi.org/10.1155/2013/298268
work_keys_str_mv AT xiaoyuzhang anovelapproachtol2lfilterdesignfortsfuzzysystemswithmultipletimevaryingdelays
AT chenggong anovelapproachtol2lfilterdesignfortsfuzzysystemswithmultipletimevaryingdelays
AT zhenzeng anovelapproachtol2lfilterdesignfortsfuzzysystemswithmultipletimevaryingdelays
AT xiaoyuzhang novelapproachtol2lfilterdesignfortsfuzzysystemswithmultipletimevaryingdelays
AT chenggong novelapproachtol2lfilterdesignfortsfuzzysystemswithmultipletimevaryingdelays
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