Stochastic stability properties of jump linear systems
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relat...
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| Published in | IEEE transactions on automatic control Vol. 37; no. 1; pp. 38 - 53 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Legacy CDMS
IEEE
01.01.1992
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 |
| DOI | 10.1109/9.109637 |
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| Abstract | Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/.< > |
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| AbstractList | Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. (I.E.) Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta-moment stability is monotonically converging to the region for almost sure stability at delta{downwards arrow}0( ) Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/.< > |
| Audience | PUBLIC |
| Author | Ji, Y. Feng, X. Chizeck, H.J. Loparo, K.A. |
| Author_xml | – sequence: 1 givenname: X. surname: Feng fullname: Feng, X. organization: Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA – sequence: 2 givenname: K.A. surname: Loparo fullname: Loparo, K.A. organization: Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA – sequence: 3 givenname: Y. surname: Ji fullname: Ji, Y. organization: Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA – sequence: 4 givenname: H.J. surname: Chizeck fullname: Chizeck, H.J. organization: Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5204090$$DView record in Pascal Francis |
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| CODEN | IETAA9 |
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| Cites_doi | 10.1109/TAC.1987.1104526 10.1002/cpa.3160270303 10.1016/0167-6911(88)90098-9 10.1109/TAC.1985.1104077 10.1137/0153017 10.1109/9.182475 10.1080/00207178508933397 10.1016/0005-1098(87)90098-7 10.1080/00207178908559680 10.1080/07362999108809223 10.1080/00207178808906192 10.1109/TAC.1969.1099088 10.1109/21.31033 10.21236/AD0274305 10.1137/0150044 10.1137/0127049 10.1109/9.35284 10.1137/1112019 10.1016/0005-1098(69)90060-0 10.1016/0022-247X(65)90130-7 10.1109/9.57016 10.1007/978-94-009-9121-7 10.1109/TAC.1960.1105035 10.1080/00207178608933459 10.1137/0144057 |
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| References | ref13 ref12 ref37 ref15 ref36 ref14 ref31 ref30 krasovskii (ref20a) 1961; 22 ref33 ref32 wonham (ref22) 1971; 2 ref19 ref18 (ref11) 1984 (ref20b) 1961; 22 bharucha (ref8) 1961 ref24 hijab (ref38) 1986 taylor (ref35) 1984 ref23 darkhovskii (ref9) 1971; 32 ji (ref26) 1990; 6 ref25 doob (ref34) 1953 ref21 (ref10) 1984 ref28 ref27 ji (ref16) 1991; 7 rosenbloom (ref6) 1955 ref29 ref7 ref4 ref3 ref5 kozin (ref1) 1969; 5 kushner (ref2) 1967 kozin (ref17) 1977 (ref20c) 1961; 22 |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Control system analysis Control systems Control theory. Systems Controllability Cybernetics Exact sciences and technology Linear systems Optimal control Stability State feedback Stochastic resonance Stochastic systems Sufficient conditions Testing |
| Title | Stochastic stability properties of jump linear systems |
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