A numerical algorithm for solving the absolute stability problem in ℝ3

Michael Margaliot; Christos Yfoulis

doi:10.1109/CDC.2005.1583290

A numerical algorithm for solving the absolute stability problem in ℝ³

Michael Margaliot, Christos Yfoulis

School of Electrical Engineering

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

Abstract

The problem of absolute stability is one of the oldest open problems in the theory of control. For low-order systems, the most general results were obtained by Pyatnitskiy and Rapoport. They derived an implicit characterization of the "most destabilizing" nonlinearity using the maximum principle. In this paper, we show that their approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.

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	7009-7013
Number of pages	5
DOIs	https://doi.org/10.1109/CDC.2005.1583290
State	Published - 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

Keywords

Differential inclusions
Global asymptotic stability under arbitrary switching
Switched controllers
Switched linear systems

Access to Document

10.1109/CDC.2005.1583290

Cite this

Margaliot, M., & Yfoulis, C. (2005). A numerical algorithm for solving the absolute stability problem in ℝ³. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 7009-7013). [1583290] (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.2005.1583290

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abstract = "The problem of absolute stability is one of the oldest open problems in the theory of control. For low-order systems, the most general results were obtained by Pyatnitskiy and Rapoport. They derived an implicit characterization of the {"}most destabilizing{"} nonlinearity using the maximum principle. In this paper, we show that their approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.",

keywords = "Differential inclusions, Global asymptotic stability under arbitrary switching, Switched controllers, Switched linear systems",

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Margaliot, M & Yfoulis, C 2005, A numerical algorithm for solving the absolute stability problem in ℝ³. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583290, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 7009-7013, 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.2005.1583290

A numerical algorithm for solving the absolute stability problem in ℝ³. / Margaliot, Michael; Yfoulis, Christos.

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7009-7013 1583290 (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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Margaliot M, Yfoulis C. A numerical algorithm for solving the absolute stability problem in ℝ³. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7009-7013. 1583290. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). https://doi.org/10.1109/CDC.2005.1583290