Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

Ahmet Cetinkaya; Kenji Kashima; Tomohisa Hayakawa

doi:10.1109/CDC.2010.5718189

Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

Ahmet Cetinkaya, Kenji Kashima, Tomohisa Hayakawa

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

7 Citations (Scopus)

Abstract

Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

Original language	English
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2378-2383
Number of pages	6
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5718189
Publication status	Published - 2010
Externally published	Yes
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: 2010 Dec 15 → 2010 Dec 17

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	10/12/15 → 10/12/17

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2010.5718189

Cite this

Cetinkaya, A., Kashima, K., & Hayakawa, T. (2010). Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 2378-2383). Article 5718189 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2010.5718189

Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps. / Cetinkaya, Ahmet; Kashima, Kenji; Hayakawa, Tomohisa.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 2378-2383 5718189 (Proceedings of the IEEE Conference on Decision and Control).

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

Cetinkaya, A, Kashima, K & Hayakawa, T 2010, Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5718189, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2378-2383, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 10/12/15. https://doi.org/10.1109/CDC.2010.5718189

Cetinkaya A, Kashima K, Hayakawa T. Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc. 2010. p. 2378-2383. 5718189. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2010.5718189

@inproceedings{85fec911132c4d76899df1e5ea7f97a8,

title = "Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps",

abstract = "Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.",

author = "Ahmet Cetinkaya and Kenji Kashima and Tomohisa Hayakawa",

year = "2010",

doi = "10.1109/CDC.2010.5718189",

language = "English",

isbn = "9781424477456",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "2378--2383",

booktitle = "2010 49th IEEE Conference on Decision and Control, CDC 2010",

note = "49th IEEE Conference on Decision and Control, CDC 2010 ; Conference date: 15-12-2010 Through 17-12-2010",

}

TY - GEN

T1 - Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

AU - Cetinkaya, Ahmet

AU - Kashima, Kenji

AU - Hayakawa, Tomohisa

PY - 2010

Y1 - 2010

N2 - Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

AB - Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

UR - http://www.scopus.com/inward/record.url?scp=79953132179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953132179&partnerID=8YFLogxK

U2 - 10.1109/CDC.2010.5718189

DO - 10.1109/CDC.2010.5718189

M3 - Conference contribution

AN - SCOPUS:79953132179

SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2378

EP - 2383

BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 49th IEEE Conference on Decision and Control, CDC 2010

Y2 - 15 December 2010 through 17 December 2010

ER -

Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this