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

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

7 Citations (Scopus)

Abstract

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

Original language	English
Title of host publication	2006 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers
Pages	899-904
Number of pages	6
ISBN (Electronic)	1-4244-0210-7
ISBN (Print)	1-4244-0209-3
DOIs	https://doi.org/10.1109/ACC.2006.1655472
Publication status	Published - 24 Jul 2006
Externally published	Yes
Event	2006 American Control Conference (ACC 2006), June 14-16, 2006, Minneapolis, MN, USA - Minneapolis, MN, USA, Minneapolis, MN, United States Duration: 14 Jun 2006 → 16 Jun 2006

Conference

Conference	2006 American Control Conference (ACC 2006), June 14-16, 2006, Minneapolis, MN, USA
Abbreviated title	ACC 2006
Country/Territory	United States
City	Minneapolis, MN
Period	14/06/06 → 16/06/06

Keywords

Linear systems
Stability analysis
Algebra
Difference equations
Kernel
Automata
Random variables

Access to Document

10.1109/ACC.2006.1655472

Cite this

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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",

year = "2006",

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day = "24",

doi = "10.1109/ACC.2006.1655472",

language = "English",

isbn = "1-4244-0209-3",

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booktitle = "2006 American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers",

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note = "2006 American Control Conference (ACC 2006), June 14-16, 2006, Minneapolis, MN, USA, ACC 2006 ; Conference date: 14-06-2006 Through 16-06-2006",

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Tejada, A, Gonzalez, OR & Gray, WS 2006, On the Markov property for nonlinear discrete-time systems with Markovian inputs. in 2006 American Control Conference., 1655472, Institute of Electrical and Electronics Engineers, pp. 899-904, 2006 American Control Conference (ACC 2006), June 14-16, 2006, Minneapolis, MN, USA, Minneapolis, MN, United States, 14/06/06. https://doi.org/10.1109/ACC.2006.1655472

TY - GEN

T1 - On the Markov property for nonlinear discrete-time systems with Markovian inputs

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

Abstract

Conference

Keywords

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