State-feedback stabilization of Markov jump linear systems with randomly observed markov states

Masaki Ogura; Ahmet Cetinkaya; Victor M. Preciado

doi:10.1109/ACC.2015.7170988

State-feedback stabilization of Markov jump linear systems with randomly observed markov states

Masaki Ogura, Ahmet Cetinkaya, Victor M. Preciado

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

1 Citation (Scopus)

Abstract

In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov state space but with so-called cluster observations of Markov states. Based on this transformation we propose linear matrix inequalities for designing stabilizing state-feedback gains for the original Markov jump linear systems. The proposed method can treat both periodic observations and many of renewaltype observations in a unified manner, which are studied in the literature using different approaches. A numerical example is provided to demonstrate the obtained result.

Original language	English
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1764-1769
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7170988
Publication status	Published - 2015 Jul 28
Externally published	Yes
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: 2015 Jul 1 → 2015 Jul 3

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	15/7/1 → 15/7/3

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.2015.7170988

Cite this

Ogura, M., Cetinkaya, A., & Preciado, V. M. (2015). State-feedback stabilization of Markov jump linear systems with randomly observed markov states. In ACC 2015 - 2015 American Control Conference (pp. 1764-1769). [7170988] (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7170988

State-feedback stabilization of Markov jump linear systems with randomly observed markov states. / Ogura, Masaki; Cetinkaya, Ahmet; Preciado, Victor M.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1764-1769 7170988 (Proceedings of the American Control Conference; Vol. 2015-July).

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

Ogura, M, Cetinkaya, A & Preciado, VM 2015, State-feedback stabilization of Markov jump linear systems with randomly observed markov states. in ACC 2015 - 2015 American Control Conference., 7170988, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 1764-1769, 2015 American Control Conference, ACC 2015, Chicago, United States, 15/7/1. https://doi.org/10.1109/ACC.2015.7170988

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abstract = "In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov state space but with so-called cluster observations of Markov states. Based on this transformation we propose linear matrix inequalities for designing stabilizing state-feedback gains for the original Markov jump linear systems. The proposed method can treat both periodic observations and many of renewaltype observations in a unified manner, which are studied in the literature using different approaches. A numerical example is provided to demonstrate the obtained result.",

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N2 - In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov state space but with so-called cluster observations of Markov states. Based on this transformation we propose linear matrix inequalities for designing stabilizing state-feedback gains for the original Markov jump linear systems. The proposed method can treat both periodic observations and many of renewaltype observations in a unified manner, which are studied in the literature using different approaches. A numerical example is provided to demonstrate the obtained result.

AB - In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov state space but with so-called cluster observations of Markov states. Based on this transformation we propose linear matrix inequalities for designing stabilizing state-feedback gains for the original Markov jump linear systems. The proposed method can treat both periodic observations and many of renewaltype observations in a unified manner, which are studied in the literature using different approaches. A numerical example is provided to demonstrate the obtained result.

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State-feedback stabilization of Markov jump linear systems with randomly observed markov states

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