Classification of linear planar systems with hybrid feedback control

Elena Litsyn; Marina Myasnikova; Yurii Nepomnyashchikh; Arcady Ponosov

doi:10.1109/CDC.2005.1583208

Classification of linear planar systems with hybrid feedback control

Elena Litsyn, Marina Myasnikova, Yurii Nepomnyashchikh, Arcady Ponosov

Department of Mathematics

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

Abstract

Continuing the authors' studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical representatives in each class are determined. It is shown how to use this classification to find out whether a given system is stabilizable or not.

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	6522-6526
Number of pages	5
DOIs	https://doi.org/10.1109/CDC.2005.1583208
State	Published - 1 Dec 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

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	12/12/05 → 15/12/05

ASJC Scopus subject areas

Engineering (all)

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10.1109/CDC.2005.1583208

Cite this

Litsyn, E., Myasnikova, M., Nepomnyashchikh, Y., & Ponosov, A. (2005). Classification of linear planar systems with hybrid feedback control. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 6522-6526). [1583208] (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.2005.1583208

Litsyn, Elena ; Myasnikova, Marina ; Nepomnyashchikh, Yurii et al. / Classification of linear planar systems with hybrid feedback control. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. pp. 6522-6526 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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title = "Classification of linear planar systems with hybrid feedback control",

abstract = "Continuing the authors' studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical representatives in each class are determined. It is shown how to use this classification to find out whether a given system is stabilizable or not.",

author = "Elena Litsyn and Marina Myasnikova and Yurii Nepomnyashchikh and Arcady Ponosov",

year = "2005",

month = dec,

day = "1",

doi = "10.1109/CDC.2005.1583208",

language = "English",

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series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

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booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

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Litsyn, E, Myasnikova, M, Nepomnyashchikh, Y & Ponosov, A 2005, Classification of linear planar systems with hybrid feedback control. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583208, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 6522-6526, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583208

Classification of linear planar systems with hybrid feedback control. / Litsyn, Elena; Myasnikova, Marina; Nepomnyashchikh, Yurii et al.

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6522-6526 1583208 (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 › peer-review

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AU - Ponosov, Arcady

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AB - Continuing the authors' studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical representatives in each class are determined. It is shown how to use this classification to find out whether a given system is stabilizable or not.

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Litsyn E, Myasnikova M, Nepomnyashchikh Y, Ponosov A. Classification of linear planar systems with hybrid feedback control. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6522-6526. 1583208. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583208

Classification of linear planar systems with hybrid feedback control

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