Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems

Tao Yang, Antonie Arij Stoorvogel, Ali Saberi, Karl H. Johansson

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)

Abstract

It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.
Original languageUndefined
Title of host publicationProceedings of the European Control Conference 2013 (ECC13)
PublisherOmniPress
Pages2728-2733
Number of pages6
ISBN (Print)978-3-9524173-4-8
Publication statusPublished - 2013
Event2013 European Control Conference, ECC 2013 - Zürich, Switzerland
Duration: 17 Jul 201319 Jul 2013

Publication series

Name
PublisherOmnipress

Conference

Conference2013 European Control Conference, ECC 2013
Abbreviated titleECC
CountrySwitzerland
CityZürich
Period17/07/1319/07/13

Keywords

  • EWI-23870
  • METIS-300109
  • IR-87576

Cite this

Yang, T., Stoorvogel, A. A., Saberi, A., & Johansson, K. H. (2013). Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. In Proceedings of the European Control Conference 2013 (ECC13) (pp. 2728-2733). OmniPress.
Yang, Tao ; Stoorvogel, Antonie Arij ; Saberi, Ali ; Johansson, Karl H. / Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. Proceedings of the European Control Conference 2013 (ECC13). OmniPress, 2013. pp. 2728-2733
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Yang, T, Stoorvogel, AA, Saberi, A & Johansson, KH 2013, Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. in Proceedings of the European Control Conference 2013 (ECC13). OmniPress, pp. 2728-2733, 2013 European Control Conference, ECC 2013, Zürich, Switzerland, 17/07/13.

Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. / Yang, Tao; Stoorvogel, Antonie Arij; Saberi, Ali; Johansson, Karl H.

Proceedings of the European Control Conference 2013 (ECC13). OmniPress, 2013. p. 2728-2733.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems

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N2 - It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

AB - It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

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KW - METIS-300109

KW - IR-87576

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Yang T, Stoorvogel AA, Saberi A, Johansson KH. Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. In Proceedings of the European Control Conference 2013 (ECC13). OmniPress. 2013. p. 2728-2733