A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs

A. Tejada; O.R. Gonzalez; W.S. Gray

doi:10.1109/SSST.2006.1619071

A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs

A. Tejada
, O.R. Gonzalez
, W.S. Gray

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

1 Citaat (Scopus)

Samenvatting

The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k + 1) = F_k(x(k), thetas(k)), where thetas(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), thetas(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts

Originele taal-2	Engels
Titel	2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	328-332
Aantal pagina's	5
ISBN van geprinte versie	0-7803-9457-7
DOI's	https://doi.org/10.1109/SSST.2006.1619071
Status	Gepubliceerd - 18 apr. 2006
Extern gepubliceerd	Ja
Evenement	38th Southeastern Symposium on System Theory, SSST 2006 - Cookeville, Verenigde Staten van Amerika Duur: 5 mrt. 2006 → 7 mrt. 2006 Congresnummer: 38 http://ieeecss.org/event/38th-southeastern-symposium-system-theory

Congres

Congres	38th Southeastern Symposium on System Theory, SSST 2006
Verkorte titel	SSST 2006
Land/Regio	Verenigde Staten van Amerika
Stad	Cookeville
Periode	5/03/06 → 7/03/06
Internet adres	http://ieeecss.org/event/38th-southeastern-symposium-system-theory

Toegang tot document

10.1109/SSST.2006.1619071

Citeer dit

@inproceedings{57b5ea011df94b4cb5667287f420ed84,

title = "A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs",

abstract = "The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k + 1) = Fk(x(k), thetas(k)), where thetas(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), thetas(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts",

keywords = "Stability analysis, Random variables, Difference equations, Markov processes, Linear systems, Kernel, Particle measurements, Algebra",

author = "A. Tejada and O.R. Gonzalez and W.S. Gray",

year = "2006",

month = apr,

day = "18",

doi = "10.1109/SSST.2006.1619071",

language = "English",

isbn = "0-7803-9457-7",

pages = "328--332",

booktitle = "2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "38th Southeastern Symposium on System Theory, SSST 2006, SSST 2006 ; Conference date: 05-03-2006 Through 07-03-2006",

url = "http://ieeecss.org/event/38th-southeastern-symposium-system-theory",

}

Tejada, A, Gonzalez, OR & Gray, WS 2006, A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs. in 2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory., 1619071, Institute of Electrical and Electronics Engineers, blz. 328-332, 38th Southeastern Symposium on System Theory, SSST 2006, Cookeville, Tennessee, Verenigde Staten van Amerika, 5/03/06. https://doi.org/10.1109/SSST.2006.1619071

A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs. / Tejada, A.; Gonzalez, O.R.; Gray, W.S.
2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory. Institute of Electrical and Electronics Engineers, 2006. blz. 328-332 1619071.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs

AU - Tejada, A.

AU - Gonzalez, O.R.

AU - Gray, W.S.

N1 - Conference code: 38

PY - 2006/4/18

Y1 - 2006/4/18

N2 - The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k + 1) = Fk(x(k), thetas(k)), where thetas(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), thetas(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts

AB - The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k + 1) = Fk(x(k), thetas(k)), where thetas(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), thetas(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts

KW - Stability analysis

KW - Random variables

KW - Difference equations

KW - Markov processes

KW - Linear systems

KW - Kernel

KW - Particle measurements

KW - Algebra

U2 - 10.1109/SSST.2006.1619071

DO - 10.1109/SSST.2006.1619071

M3 - Conference contribution

SN - 0-7803-9457-7

SP - 328

EP - 332

BT - 2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory

PB - Institute of Electrical and Electronics Engineers

T2 - 38th Southeastern Symposium on System Theory, SSST 2006

Y2 - 5 March 2006 through 7 March 2006

ER -

A measure-theoretic proof of the Markov property for hybrid systems with Markovian inputs

Samenvatting

Congres

Toegang tot document

Vingerafdruk

Citeer dit