Stochastic stability of semi-Markovian jump systems with mode-dependent delays
SUMMARYSemi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a...
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| Published in | International journal of robust and nonlinear control Vol. 24; no. 18; pp. 3317 - 3330 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Bognor Regis
Blackwell Publishing Ltd
01.12.2014
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1049-8923 1099-1239 |
| DOI | 10.1002/rnc.3057 |
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| Abstract | SUMMARYSemi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd. |
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| AbstractList | Semi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd. SUMMARY Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi-Markovian systems with mode-dependent time-variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time-delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd. Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi-Markovian systems with mode-dependent time-variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time-delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright copyright 2013 John Wiley & Sons, Ltd. SUMMARYSemi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi‐Markovian systems with mode‐dependent time‐variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time‐delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd. |
| Author | Shi, Peng Li, Fanbiao Wu, Ligang |
| Author_xml | – sequence: 1 givenname: Fanbiao surname: Li fullname: Li, Fanbiao organization: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, 150001, Harbin, China – sequence: 2 givenname: Ligang surname: Wu fullname: Wu, Ligang email: Correspondence to: Ligang Wu, Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, China., ligangwu@hit.edu.cn organization: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, 150001, Harbin, China – sequence: 3 givenname: Peng surname: Shi fullname: Shi, Peng organization: School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005, Adelaide, Australia |
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| Snippet | SUMMARYSemi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe... Semi‐Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a... SUMMARY Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to... Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a... |
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| SubjectTerms | Delay Dynamical systems Lyapunov functions Markov processes mode-dependent time-delays Nonlinear dynamics semi-Markovian jump systems Stability Stochastic processes stochastic stability Stochasticity |
| Title | Stochastic stability of semi-Markovian jump systems with mode-dependent delays |
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