Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates

Sung Hyun Kim; Ngoc Hoai An Nguyen

doi:10.1109/ICCAS.2015.7364780

Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates

Sung Hyun Kim
, Ngoc Hoai An Nguyen

Department of Industrial and Systems Engineering

University of Ulsan

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

1 Scopus citations

Abstract

This paper investigates the stochastic stability analysis problem for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs). To this end, the stability condition for S-MJLSs is first formulated in the form of two set constraints and a matrix inequality dependent on the time-varying transition rates stemming from sojourn time. And then, the sojourn-time-dependent stability condition is converted into a finite set of linear matrix inequalities (LMIs) via the use of a relaxation technique capable of considering all possible constraints associated with time-varying transition rates.

Original language	English
Title of host publication	ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	995-998
Number of pages	4
ISBN (Electronic)	9788993215090
DOIs	https://doi.org/10.1109/ICCAS.2015.7364780
State	Published - 23 Dec 2015
Event	15th International Conference on Control, Automation and Systems, ICCAS 2015 - Busan, Korea, Republic of Duration: 13 Oct 2015 → 16 Oct 2015

Publication series

Name	ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings

Conference

Conference	15th International Conference on Control, Automation and Systems, ICCAS 2015
Country/Territory	Korea, Republic of
City	Busan
Period	13/10/15 → 16/10/15

Keywords

relaxation technique
semi-Markovian jump systems
Stochastic stability analysis

Access to Document

10.1109/ICCAS.2015.7364780

Cite this

Kim, S. H., & Nguyen, N. H. A. (2015). Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates. In ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings (pp. 995-998). Article 7364780 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICCAS.2015.7364780

Kim, Sung Hyun ; Nguyen, Ngoc Hoai An. / Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates. ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 995-998 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings).

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title = "Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates",

abstract = "This paper investigates the stochastic stability analysis problem for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs). To this end, the stability condition for S-MJLSs is first formulated in the form of two set constraints and a matrix inequality dependent on the time-varying transition rates stemming from sojourn time. And then, the sojourn-time-dependent stability condition is converted into a finite set of linear matrix inequalities (LMIs) via the use of a relaxation technique capable of considering all possible constraints associated with time-varying transition rates.",

keywords = "relaxation technique, semi-Markovian jump systems, Stochastic stability analysis",

author = "Kim, \{Sung Hyun\} and Nguyen, \{Ngoc Hoai An\}",

note = "Publisher Copyright: {\textcopyright} 2015 Institute of Control, Robotics and Systems - ICROS.; 15th International Conference on Control, Automation and Systems, ICCAS 2015 ; Conference date: 13-10-2015 Through 16-10-2015",

year = "2015",

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doi = "10.1109/ICCAS.2015.7364780",

language = "English",

series = "ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings",

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Kim, SH & Nguyen, NHA 2015, Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates. in ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings., 7364780, ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 995-998, 15th International Conference on Control, Automation and Systems, ICCAS 2015, Busan, Korea, Republic of, 13/10/15. https://doi.org/10.1109/ICCAS.2015.7364780

Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates. / Kim, Sung Hyun; Nguyen, Ngoc Hoai An.
ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. p. 995-998 7364780 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings).

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

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AU - Nguyen, Ngoc Hoai An

PY - 2015/12/23

Y1 - 2015/12/23

N2 - This paper investigates the stochastic stability analysis problem for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs). To this end, the stability condition for S-MJLSs is first formulated in the form of two set constraints and a matrix inequality dependent on the time-varying transition rates stemming from sojourn time. And then, the sojourn-time-dependent stability condition is converted into a finite set of linear matrix inequalities (LMIs) via the use of a relaxation technique capable of considering all possible constraints associated with time-varying transition rates.

AB - This paper investigates the stochastic stability analysis problem for a class of continuous-time semi-Markovian jump linear systems (S-MJLSs). To this end, the stability condition for S-MJLSs is first formulated in the form of two set constraints and a matrix inequality dependent on the time-varying transition rates stemming from sojourn time. And then, the sojourn-time-dependent stability condition is converted into a finite set of linear matrix inequalities (LMIs) via the use of a relaxation technique capable of considering all possible constraints associated with time-varying transition rates.

KW - relaxation technique

KW - semi-Markovian jump systems

KW - Stochastic stability analysis

UR - https://www.scopus.com/pages/publications/84966405143

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DO - 10.1109/ICCAS.2015.7364780

M3 - Conference contribution

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EP - 998

BT - ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 15th International Conference on Control, Automation and Systems, ICCAS 2015

Y2 - 13 October 2015 through 16 October 2015

ER -

Kim SH, Nguyen NHA. Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates. In ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc. 2015. p. 995-998. 7364780. (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings). doi: 10.1109/ICCAS.2015.7364780

Stochastic stability analysis of semi-Markovian jump linear systems via a relaxation technique for time-varying transition rates

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