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Phase Limitations of Zames-Falb Multipliers

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Phase Limitations of Zames-Falb Multipliers. / Wang, Shuai; Carrasco, Joaquin; Heath, William P.
In: IEEE Transactions on Automatic Control, Vol. 63, No. 4, 01.04.2018, p. 947-959.

Research output: Contribution to journal › Article › peer-review

HarvardHarvard

Wang, S, Carrasco, J & Heath, WP 2018, 'Phase Limitations of Zames-Falb Multipliers', IEEE Transactions on Automatic Control, vol. 63, no. 4, pp. 947-959. https://doi.org/10.1109/tac.2017.2729162

APA

Wang, S., Carrasco, J., & Heath, W. P. (2018). Phase Limitations of Zames-Falb Multipliers. IEEE Transactions on Automatic Control, 63(4), 947-959. https://doi.org/10.1109/tac.2017.2729162

CBE

Wang S, Carrasco J, Heath WP. 2018. Phase Limitations of Zames-Falb Multipliers. IEEE Transactions on Automatic Control. 63(4):947-959. https://doi.org/10.1109/tac.2017.2729162

MLA

Wang, Shuai, Joaquin Carrasco, and William P. Heath. "Phase Limitations of Zames-Falb Multipliers". IEEE Transactions on Automatic Control. 2018, 63(4). 947-959. https://doi.org/10.1109/tac.2017.2729162

VancouverVancouver

Wang S, Carrasco J, Heath WP. Phase Limitations of Zames-Falb Multipliers. IEEE Transactions on Automatic Control. 2018 Apr 1;63(4):947-959. Epub 2017 Jul 19. doi: 10.1109/tac.2017.2729162

Author

Wang, Shuai ; Carrasco, Joaquin ; Heath, William P. / Phase Limitations of Zames-Falb Multipliers. In: IEEE Transactions on Automatic Control. 2018 ; Vol. 63, No. 4. pp. 947-959.

RIS

TY - JOUR

T1 - Phase Limitations of Zames-Falb Multipliers

AU - Wang, Shuai

AU - Carrasco, Joaquin

AU - Heath, William P.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Phase limitations of both continuous-time and discrete-time Zames–Falb multipliers and their relation with the Kalman conjecture are analyzed. A phase limitation for continuous-time multipliers given by Megretski is generalized and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames– Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase limitation for discrete-time Zames–Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain

AB - Phase limitations of both continuous-time and discrete-time Zames–Falb multipliers and their relation with the Kalman conjecture are analyzed. A phase limitation for continuous-time multipliers given by Megretski is generalized and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames– Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase limitation for discrete-time Zames–Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain

U2 - 10.1109/tac.2017.2729162

DO - 10.1109/tac.2017.2729162

M3 - Erthygl

VL - 63

SP - 947

EP - 959

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 2334-3303

IS - 4

ER -