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Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes
This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented....
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Published in: | IEEE transactions on cybernetics 2018-09, Vol.48 (9), p.2736-2749 |
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description | This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented. |
doi_str_mv | 10.1109/TCYB.2017.2749244 |
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A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. 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(IEEE) 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c392t-13935cafc38b18945d320847cb496f238f582e934706719e08ab7ecc91e2c95d3</citedby><cites>FETCH-LOGICAL-c392t-13935cafc38b18945d320847cb496f238f582e934706719e08ab7ecc91e2c95d3</cites><orcidid>0000-0002-9122-7184 ; 0000-0002-9749-7580</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8046138$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>315,783,787,27936,27937,55124</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/28945605$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Jinghao Li</creatorcontrib><creatorcontrib>Qingling Zhang</creatorcontrib><creatorcontrib>Xing-Gang Yan</creatorcontrib><creatorcontrib>Spurgeon, Sarah K.</creatorcontrib><title>Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes</title><title>IEEE transactions on cybernetics</title><addtitle>TCYB</addtitle><addtitle>IEEE Trans Cybern</addtitle><description>This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.</description><subject>Control stability</subject><subject>Control systems</subject><subject>Fuzzy control</subject><subject>Fuzzy systems</subject><subject>Integral sliding mode control</subject><subject>Integrals</subject><subject>inverted pendulum</subject><subject>Linear matrix inequalities</subject><subject>Lyapunov methods</subject><subject>Mathematical models</subject><subject>Matrix methods</subject><subject>Motion stability</subject><subject>nonparallel distributed compensation (Non-PDC)</subject><subject>Robust stabilization</subject><subject>Robustness</subject><subject>Robustness (mathematics)</subject><subject>Sliding mode control</subject><subject>Stability analysis</subject><subject>Stochastic processes</subject><subject>Stochastic systems</subject><subject>Symmetric matrices</subject><subject>Takagi–Sugeno (T–S) fuzzy stochastic descriptor systems</subject><issn>2168-2267</issn><issn>2168-2275</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNpdkE1rGzEQQEVoSEKaHxACRdBLLuvqa1fSMXGaNpAQqN1DexFaeTZVWK8cSVuwf31k7PrQucww82YYHkKXlEwoJfrLfPrrdsIIlRMmhWZCHKEzRhtVMSbrD4e6kafoIqVXUkKVllYn6JQpLeqG1Gfo94_QjinjWbat7_3GZh8GHDo8r2b4ftxs1mUU3B-bsnf4DpKLfpVDxLN1yrBM-K-3-GHI8BJtj2e9X_jhBT-FBaSP6LizfYKLfT5HP--_zqffq8fnbw_Tm8fKcc1yRbnmtbOd46ql278WnBElpGuFbjrGVVcrBpoLSRpJNRBlWwnOaQrM6UKfo-vd3VUMbyOkbJY-Oeh7O0AYk6FacKbqhouCfv4PfQ1jHMp3hlEqqSCE14WiO8rFkFKEzqyiX9q4NpSYrXuzdW-27s3efdn5tL88tktYHDb-mS7A1Q7wAHAYKyIayhV_B0HMhlc</recordid><startdate>20180901</startdate><enddate>20180901</enddate><creator>Jinghao Li</creator><creator>Qingling Zhang</creator><creator>Xing-Gang Yan</creator><creator>Spurgeon, Sarah K.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-9122-7184</orcidid><orcidid>https://orcid.org/0000-0002-9749-7580</orcidid></search><sort><creationdate>20180901</creationdate><title>Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes</title><author>Jinghao Li ; Qingling Zhang ; Xing-Gang Yan ; Spurgeon, Sarah K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-13935cafc38b18945d320847cb496f238f582e934706719e08ab7ecc91e2c95d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Control stability</topic><topic>Control systems</topic><topic>Fuzzy control</topic><topic>Fuzzy systems</topic><topic>Integral sliding mode control</topic><topic>Integrals</topic><topic>inverted pendulum</topic><topic>Linear matrix inequalities</topic><topic>Lyapunov methods</topic><topic>Mathematical models</topic><topic>Matrix methods</topic><topic>Motion stability</topic><topic>nonparallel distributed compensation (Non-PDC)</topic><topic>Robust stabilization</topic><topic>Robustness</topic><topic>Robustness (mathematics)</topic><topic>Sliding mode control</topic><topic>Stability analysis</topic><topic>Stochastic processes</topic><topic>Stochastic systems</topic><topic>Symmetric matrices</topic><topic>Takagi–Sugeno (T–S) fuzzy stochastic descriptor systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jinghao Li</creatorcontrib><creatorcontrib>Qingling Zhang</creatorcontrib><creatorcontrib>Xing-Gang Yan</creatorcontrib><creatorcontrib>Spurgeon, Sarah K.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Electronic Library Online</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transactions on cybernetics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jinghao Li</au><au>Qingling Zhang</au><au>Xing-Gang Yan</au><au>Spurgeon, Sarah K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes</atitle><jtitle>IEEE transactions on cybernetics</jtitle><stitle>TCYB</stitle><addtitle>IEEE Trans Cybern</addtitle><date>2018-09-01</date><risdate>2018</risdate><volume>48</volume><issue>9</issue><spage>2736</spage><epage>2749</epage><pages>2736-2749</pages><issn>2168-2267</issn><eissn>2168-2275</eissn><coden>ITCEB8</coden><abstract>This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. 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subjects | Control stability Control systems Fuzzy control Fuzzy systems Integral sliding mode control Integrals inverted pendulum Linear matrix inequalities Lyapunov methods Mathematical models Matrix methods Motion stability nonparallel distributed compensation (Non-PDC) Robust stabilization Robustness Robustness (mathematics) Sliding mode control Stability analysis Stochastic processes Stochastic systems Symmetric matrices Takagi–Sugeno (T–S) fuzzy stochastic descriptor systems |
title | Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes |
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