Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process

Ahmet Cetinkaya; Tomohisa Hayakawa

doi:10.1109/acc.2011.5991013

Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process

Ahmet Cetinkaya, Tomohisa Hayakawa

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

2 Citations (Scopus)

Abstract

Stability conditions of continuous-time switched stochastic dynamical systems driven by a Brownian motion and a Markov modulated compound Poisson process are provided. The mode signal, which manages the transition between subsystems, is modeled as a Markov chain. The state variables of the switched stochastic system are subject to jumps of random size occurring at random instances. The intensity of the occurrences, as well as the size of these jumps are modulated by the mode signal. A comparison approach is employed to show the almost sure asymptotic stability of the zero solution. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

Original language	English
Title of host publication	Proceedings of the 2011 American Control Conference, ACC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1458-1463
Number of pages	6
ISBN (Print)	9781457700804
DOIs	https://doi.org/10.1109/acc.2011.5991013
Publication status	Published - 2011
Externally published	Yes

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2011.5991013

Cite this

Cetinkaya, A., & Hayakawa, T. (2011). Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process. In Proceedings of the 2011 American Control Conference, ACC 2011 (pp. 1458-1463). [5991013] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2011.5991013

Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process. / Cetinkaya, Ahmet; Hayakawa, Tomohisa.
Proceedings of the 2011 American Control Conference, ACC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 1458-1463 5991013 (Proceedings of the American Control Conference).

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

Cetinkaya, A & Hayakawa, T 2011, Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process. in Proceedings of the 2011 American Control Conference, ACC 2011., 5991013, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1458-1463. https://doi.org/10.1109/acc.2011.5991013

Cetinkaya A, Hayakawa T. Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process. In Proceedings of the 2011 American Control Conference, ACC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 1458-1463. 5991013. (Proceedings of the American Control Conference). doi: 10.1109/acc.2011.5991013

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abstract = "Stability conditions of continuous-time switched stochastic dynamical systems driven by a Brownian motion and a Markov modulated compound Poisson process are provided. The mode signal, which manages the transition between subsystems, is modeled as a Markov chain. The state variables of the switched stochastic system are subject to jumps of random size occurring at random instances. The intensity of the occurrences, as well as the size of these jumps are modulated by the mode signal. A comparison approach is employed to show the almost sure asymptotic stability of the zero solution. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.",

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AB - Stability conditions of continuous-time switched stochastic dynamical systems driven by a Brownian motion and a Markov modulated compound Poisson process are provided. The mode signal, which manages the transition between subsystems, is modeled as a Markov chain. The state variables of the switched stochastic system are subject to jumps of random size occurring at random instances. The intensity of the occurrences, as well as the size of these jumps are modulated by the mode signal. A comparison approach is employed to show the almost sure asymptotic stability of the zero solution. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

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Stability of switched stochastic dynamical systems driven by Brownian motion and Markov modulated compound poisson process

Abstract

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