Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method

Guisheng Zhai; Hideaki Kondo; Joe Imae; Tomoaki Kobayashi

doi:10.1109/CDC.2005.1583274

Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method

Guisheng Zhai, Hideaki Kondo, Joe Imae, Tomoaki Kobayashi

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

1 Citation (Scopus)

Abstract

For two-dimensional linear time-invariant (LTI) systems which are not stabilizable via a single static output feedback, we propose a hybrid stabilization strategy based on a geometric method. More precisely, we design two static output feedback gains and a switching law between the feedback gains so that the entire closed-loop system is asymptotically stable. The proposed switching law is composed of output-dependent switching and time-controlled switching. We demonstrate the design method with various examples, and show that in some cases the stabilizability depends on the region of the initial state, while in other cases the system Is globally stabilizable.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	6911-6916
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1583274
Publication status	Published - 2005
Externally published	Yes
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 2005 Dec 12 → 2005 Dec 15

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	05/12/12 → 05/12/15

Keywords

Asymptotic line
Hybrid stabilization
Output-dependent switching
Static output feedback
Switching line
Time-controlled switching
Two-dimensional LTI system

ASJC Scopus subject areas

Engineering(all)

Access to Document

10.1109/CDC.2005.1583274

Cite this

Zhai, G., Kondo, H., Imae, J., & Kobayashi, T. (2005). Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 6911-6916). [1583274] (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583274

Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method. / Zhai, Guisheng; Kondo, Hideaki; Imae, Joe et al.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6911-6916 1583274 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

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

Zhai, G, Kondo, H, Imae, J & Kobayashi, T 2005, Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583274, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 6911-6916, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 05/12/12. https://doi.org/10.1109/CDC.2005.1583274

Zhai G, Kondo H, Imae J, Kobayashi T. Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6911-6916. 1583274. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583274

Zhai, Guisheng ; Kondo, Hideaki ; Imae, Joe et al. / Hybrid static output feedback stabilization of two-dimensional LTI systems : A geometric method. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. pp. 6911-6916 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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abstract = "For two-dimensional linear time-invariant (LTI) systems which are not stabilizable via a single static output feedback, we propose a hybrid stabilization strategy based on a geometric method. More precisely, we design two static output feedback gains and a switching law between the feedback gains so that the entire closed-loop system is asymptotically stable. The proposed switching law is composed of output-dependent switching and time-controlled switching. We demonstrate the design method with various examples, and show that in some cases the stabilizability depends on the region of the initial state, while in other cases the system Is globally stabilizable.",

keywords = "Asymptotic line, Hybrid stabilization, Output-dependent switching, Static output feedback, Switching line, Time-controlled switching, Two-dimensional LTI system",

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AB - For two-dimensional linear time-invariant (LTI) systems which are not stabilizable via a single static output feedback, we propose a hybrid stabilization strategy based on a geometric method. More precisely, we design two static output feedback gains and a switching law between the feedback gains so that the entire closed-loop system is asymptotically stable. The proposed switching law is composed of output-dependent switching and time-controlled switching. We demonstrate the design method with various examples, and show that in some cases the stabilizability depends on the region of the initial state, while in other cases the system Is globally stabilizable.

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Hybrid static output feedback stabilization of two-dimensional LTI systems: A geometric method

Abstract

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Keywords

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