State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems
This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stocha...
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| Published in | IEEE transactions on automatic control Vol. 55; no. 5; pp. 1213 - 1219 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.05.2010
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system. Then, the sliding-mode control problem is considered by designing an integral sliding surface function. An observer is designed to estimate the system states, and a sliding-mode control scheme is synthesized for the reaching motion based on the state estimates. It is shown that the sliding mode in the estimation space can be attained in a finite time. Some conditions for the stochastic admissibility of the overall closed-loop system are derived. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory. |
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| AbstractList | This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system. Then, the sliding-mode control problem is considered by designing an integral sliding surface function. An observer is designed to estimate the system states, and a sliding-mode control scheme is synthesized for the reaching motion based on the state estimates. It is shown that the sliding mode in the estimation space can be attained in a finite time. Some conditions for the stochastic admissibility of the overall closed-loop system are derived. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory. |
| Author | Peng Shi Ligang Wu Huijun Gao |
| Author_xml | – sequence: 1 givenname: Ligang surname: Wu fullname: Wu, Ligang – sequence: 2 givenname: Peng surname: Shi fullname: Shi, Peng – sequence: 3 givenname: Huijun surname: Gao fullname: Gao, Huijun |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23118141$$DView record in Pascal Francis |
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| CODEN | IETAA9 |
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| Cites_doi | 10.1109/TAC.2003.817012 10.1109/ICCA.2007.4376898 10.1049/iet-cta:20060479 10.1109/LSP.2004.831729 10.1002/acs.1030 10.1080/00207170701203608 10.1016/j.automatica.2009.05.014 10.1016/j.automatica.2007.10.027 10.1016/j.sysconle.2006.03.007 10.1109/TSP.2003.815382 10.1109/TAC.2006.875017 10.1016/j.automatica.2007.02.023 10.1109/9.780431 10.1007/BFb0002475 10.1109/TAC.2005.861716 10.1109/TAC.2002.800651 10.1016/j.automatica.2005.12.015 10.1002/oca.780 10.1016/j.jfranklin.2007.09.001 10.1007/978-3-642-84379-2 10.1016/j.na.2005.05.066 10.1109/9.995042 |
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| Keywords | Markov process Singularity singular systems sliding-mode control Admissibility Markovian system Probabilistic approach Variable structure control Necessary and sufficient condition Sliding mode Variable structure system Continuous time Closed feedback unmeasured states Observer Linear matrix inequality Jump process System identification Jumping State estimation Markovian jump |
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| References | ref13 guo (ref4) 2008 ref15 ref14 xu (ref26) 2006 ref10 ref2 ref1 ref17 ref16 ref19 uezato (ref12) 1999 wei (ref18) 2007; 80 zhong (ref29) 2007; 3 wu (ref21) 2008; 44 zhong (ref28) 2008; 4 ref24 ref23 ref25 ref20 ref22 ref27 qiu (ref8) 2009; 3 ref7 ref9 ref3 ref6 sun (ref11) 2009; 5 ref5 |
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| SubjectTerms | Algorithm design and analysis Applied sciences Automatic control Computer science; control theory; systems Control system analysis Control systems Control theory. Systems Convergence Distributed algorithms Estimates Exact sciences and technology H infinity control Markovian jump Mathematical analysis Modelling and identification Motion estimation observer Observers singular systems Sliding mode Sliding mode control State estimation Stochastic systems Stochasticity Terrain factors unmeasured states Wireless sensor networks |
| Title | State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems |
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