On the Markov property for nonlinear discrete-time systems with Markovian inputs

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

doi:10.1109/ACC.2006.1655472

On the Markov property for nonlinear discrete-time systems with Markovian inputs

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

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

7 Citaten (Scopus)

Samenvatting

The behavior of a general hybrid system in discrete-time can be represented by a nonlinear 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 fundamental measure-theoretical concepts

Originele taal-2	Engels
Titel	2006 American Control Conference
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	899-904
Aantal pagina's	6
ISBN van elektronische versie	1-4244-0210-7
ISBN van geprinte versie	1-4244-0209-3
DOI's	https://doi.org/10.1109/ACC.2006.1655472
Status	Gepubliceerd - 24 jul. 2006
Extern gepubliceerd	Ja
Evenement	2006 American Control Conference - Minneapolis, MN, USA, Minneapolis, MN, Verenigde Staten van Amerika Duur: 14 jun. 2006 → 16 jun. 2006

Congres

Congres	2006 American Control Conference
Verkorte titel	ACC 2006
Land/Regio	Verenigde Staten van Amerika
Stad	Minneapolis, MN
Periode	14/06/06 → 16/06/06
Ander	2006 American Control Conference

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10.1109/ACC.2006.1655472

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title = "On the Markov property for nonlinear discrete-time systems with Markovian inputs",

abstract = "The behavior of a general hybrid system in discrete-time can be represented by a nonlinear 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 fundamental measure-theoretical concepts",

keywords = "Linear systems, Stability analysis, Algebra, Difference equations, Kernel, Automata, Random variables",

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

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AU - Tejada, A.

AU - Gonzalez, O.R.

AU - Gray, W.S.

PY - 2006/7/24

Y1 - 2006/7/24

N2 - The behavior of a general hybrid system in discrete-time can be represented by a nonlinear 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 fundamental measure-theoretical concepts

AB - The behavior of a general hybrid system in discrete-time can be represented by a nonlinear 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 fundamental measure-theoretical concepts

KW - Linear systems

KW - Stability analysis

KW - Algebra

KW - Difference equations

KW - Kernel

KW - Automata

KW - Random variables

U2 - 10.1109/ACC.2006.1655472

DO - 10.1109/ACC.2006.1655472

M3 - Conference contribution

SN - 1-4244-0209-3

SP - 899

EP - 904

BT - 2006 American Control Conference

PB - Institute of Electrical and Electronics Engineers

T2 - 2006 American Control Conference (ACC 2006), June 14-16, 2006, Minneapolis, MN, USA

Y2 - 14 June 2006 through 16 June 2006

ER -

On the Markov property for nonlinear discrete-time systems with Markovian inputs

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