SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems
In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface...
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| Published in | IEEE transactions on automatic control Vol. 63; no. 1; pp. 219 - 224 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.01.2018
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system. |
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| AbstractList | In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system. |
| Author | Pingfang Zhou Yueying Wang Yuanqing Xia Hao Shen |
| Author_xml | – sequence: 1 givenname: Yueying orcidid: 0000-0001-9737-6765 surname: Wang fullname: Wang, Yueying – sequence: 2 givenname: Yuanqing orcidid: 0000-0002-5977-4911 surname: Xia fullname: Xia, Yuanqing – sequence: 3 givenname: Hao orcidid: 0000-0001-7024-6573 surname: Shen fullname: Shen, Hao – sequence: 4 givenname: Pingfang orcidid: 0000-0001-8887-5845 surname: Zhou fullname: Zhou, Pingfang |
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| CODEN | IETAA9 |
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| References_xml | – ident: ref17 doi: 10.1016/j.automatica.2014.10.065 – ident: ref12 doi: 10.1016/j.automatica.2013.02.014 – ident: ref4 doi: 10.1109/TCSI.2011.2106090 – ident: ref6 doi: 10.1016/j.jfranklin.2015.06.017 – ident: ref16 doi: 10.1109/TIE.2014.2351378 – year: 1996 ident: ref29 publication-title: Nonlinear Control Systems – ident: ref21 doi: 10.1016/j.automatica.2016.01.070 – ident: ref14 doi: 10.1109/TIE.2013.2240641 – ident: ref15 doi: 10.1109/TAC.2013.2295662 – ident: ref7 doi: 10.1109/TCYB.2014.2375957 – ident: ref10 doi: 10.1109/TAC.2008.929376 – ident: ref3 doi: 10.1016/j.automatica.2009.02.008 – ident: ref1 doi: 10.1007/BFb0002475 – ident: ref5 doi: 10.1109/TCSI.2013.2246253 – ident: ref23 doi: 10.1109/TAC.2016.2578300 – ident: ref28 doi: 10.1109/TNNLS.2016.2573853 – year: 1969 ident: ref30 publication-title: Optimization by vector space methods – ident: ref13 doi: 10.1109/TAC.2012.2211456 – ident: ref19 doi: 10.1016/j.automatica.2015.11.007 – ident: ref26 doi: 10.1007/s11071-015-2168-0 – ident: ref27 doi: 10.1109/TIE.2014.2351379 – ident: ref11 doi: 10.1016/j.jfranklin.2011.09.015 – volume: 55 start-page: 1213 year: 2010 ident: ref24 article-title: State estimation and sliding-mode control of Markovian jump singular systems publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2010.2042234 – ident: ref18 doi: 10.1016/j.automatica.2014.10.095 – ident: ref9 doi: 10.1109/TAC.2005.861716 – ident: ref20 doi: 10.1016/j.automatica.2015.11.037 – ident: ref25 doi: 10.1016/j.automatica.2012.05.064 – year: 2006 ident: ref2 publication-title: Robust Control and Filtering of Singular Systems – ident: ref8 doi: 10.1109/9.898702 – ident: ref22 doi: 10.1109/TIE.2016.2610400 |
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| Snippet | In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to... |
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| StartPage | 219 |
| SubjectTerms | Aerodynamics Fuzzy sliding surface Integrated circuit modeling Markovian jump singular systems (MJSS) Power system dynamics Robustness Sliding mode control sliding-mode control (SMC) Stochastic processes T–S fuzzy models Uncertainty |
| Title | SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems |
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| Volume | 63 |
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