Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach

Chun Zhang; Geir E. Dullerud

doi:10.1109/CDC.2009.5400361

Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach

Chun Zhang
, Geir E. Dullerud

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

2 Scopus citations

Abstract

In this paper, we investigate the almost sure uniform exponential stabilization problem of Markovian jump linear systems (MJLSs) with logarithmically quantized state feedbacks. We introduce the concept and provide explicit constructions of finite path-dependent stabilizing logarithmic quantizers and controllers. We also present a semi-convex algorithm to determine the optimal (coarsest) stabilizing quantization density. As an example, we show that the problem of almost sure uniform stabilization of a linear time-invariant (LTI) system with quantized feedbacks over a lossy channel can be tackled under this framework. A contribution of this work is to provide a systematic approach to simultaneously treat multiple channel constraints in the feedback loop.

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2094-2099
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400361
State	Published - 2009
Externally published	Yes
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

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

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

Publisher link

10.1109/CDC.2009.5400361

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Zhang, C., & Dullerud, G. E. (2009). Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 2094-2099). Article 5400361 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400361

Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach. / Zhang, Chun; Dullerud, Geir E.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 2094-2099 5400361 (Proceedings of the IEEE Conference on Decision and Control).

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

Zhang, C & Dullerud, GE 2009, Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400361, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2094-2099, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5400361

Zhang C, Dullerud GE. Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 2094-2099. 5400361. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400361

Zhang, Chun ; Dullerud, Geir E. / Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 2094-2099 (Proceedings of the IEEE Conference on Decision and Control).

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title = "Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach",

abstract = "In this paper, we investigate the almost sure uniform exponential stabilization problem of Markovian jump linear systems (MJLSs) with logarithmically quantized state feedbacks. We introduce the concept and provide explicit constructions of finite path-dependent stabilizing logarithmic quantizers and controllers. We also present a semi-convex algorithm to determine the optimal (coarsest) stabilizing quantization density. As an example, we show that the problem of almost sure uniform stabilization of a linear time-invariant (LTI) system with quantized feedbacks over a lossy channel can be tackled under this framework. A contribution of this work is to provide a systematic approach to simultaneously treat multiple channel constraints in the feedback loop.",

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AB - In this paper, we investigate the almost sure uniform exponential stabilization problem of Markovian jump linear systems (MJLSs) with logarithmically quantized state feedbacks. We introduce the concept and provide explicit constructions of finite path-dependent stabilizing logarithmic quantizers and controllers. We also present a semi-convex algorithm to determine the optimal (coarsest) stabilizing quantization density. As an example, we show that the problem of almost sure uniform stabilization of a linear time-invariant (LTI) system with quantized feedbacks over a lossy channel can be tackled under this framework. A contribution of this work is to provide a systematic approach to simultaneously treat multiple channel constraints in the feedback loop.

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Uniform Stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach

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