Pre-specified performance based model reduction for time-varying delay systems in fuzzy framework

Yong-Duan SONG; Hongying ZHOU; Xiaojie SU; Lei WANG

doi:10.1016/j.ins.2015.08.031

Pre-specified performance based model reduction for time-varying delay systems in fuzzy framework

Yong-Duan SONG
, Hongying ZHOU
, Xiaojie SU^*
, Lei WANG

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

13 Citations (Scopus)

Abstract

This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

Original language	English
Pages (from-to)	206-221
Number of pages	16
Journal	Information Sciences
Volume	328
Early online date	28 Aug 2015
DOIs	https://doi.org/10.1016/j.ins.2015.08.031
Publication status	Published - 20 Jan 2016
Externally published	Yes

Funding

This work was partially supported by the National Key Basic Research Program (973), China (2012CB215202, 2014CB249200), the National Natural Science Foundation of China ( 61403048 and 61134001 ), the Fundamental Research Funds for the Central Universities (106112015CDJXY170001,CDJZR175501), and the Basic and Frontier Research Project of Chongqing (cstc2015jcyjA40005, cstc2014jcyjA90005).

Keywords

Model reduction
Projection approach
T-S fuzzy systems
Time-varying delay

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10.1016/j.ins.2015.08.031

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title = "Pre-specified performance based model reduction for time-varying delay systems in fuzzy framework",

abstract = "This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.",

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AU - SONG, Yong-Duan

AU - ZHOU, Hongying

AU - SU, Xiaojie

AU - WANG, Lei

PY - 2016/1/20

Y1 - 2016/1/20

N2 - This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

AB - This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

KW - Model reduction

KW - Projection approach

KW - T-S fuzzy systems

KW - Time-varying delay

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DO - 10.1016/j.ins.2015.08.031

M3 - Journal Article (refereed)

AN - SCOPUS:84945550468

SN - 0020-0255

VL - 328

SP - 206

EP - 221

JO - Information Sciences

JF - Information Sciences

ER -

Pre-specified performance based model reduction for time-varying delay systems in fuzzy framework

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Keywords

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