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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

Abstract

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

Original language	English
Title of host publication	2006 Proceeding of the Thirty-Eighth Southeastern Symposium on System Theory
Publisher	Institute of Electrical and Electronics Engineers
Pages	328-332
Number of pages	5
ISBN (Print)	0-7803-9457-7
DOIs	https://doi.org/10.1109/SSST.2006.1619071
Publication status	Published - 18 Apr 2006
Externally published	Yes
Event	38th Southeastern Symposium on System Theory, SSST 2006 - Cookeville, United States Duration: 5 Mar 2006 → 7 Mar 2006 Conference number: 38 http://ieeecss.org/event/38th-southeastern-symposium-system-theory

Conference

Conference	38th Southeastern Symposium on System Theory, SSST 2006
Abbreviated title	SSST 2006
Country/Territory	United States
City	Cookeville
Period	5/03/06 → 7/03/06
Internet address	http://ieeecss.org/event/38th-southeastern-symposium-system-theory

Keywords

Stability analysis
Random variables
Difference equations
Markov processes
Linear systems
Kernel
Particle measurements
Algebra

Access to Document

10.1109/SSST.2006.1619071

Cite this

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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, pp. 328-332, 38th Southeastern Symposium on System Theory, SSST 2006, Cookeville, Tennessee, United States, 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. p. 328-332 1619071.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › 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

Abstract

Conference

Keywords

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Cite this