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Convex Searches for Discrete-Time Zames-Falb Multipliers

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

Standard Standard

Convex Searches for Discrete-Time Zames-Falb Multipliers. / Carrasco, Joaquin; Heath, William P.; Zhang, Jingfan et al.
In: IEEE Transactions on Automatic Control, Vol. 65, No. 11, 01.11.2020, p. 4538-4553.

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

HarvardHarvard

Carrasco, J, Heath, WP, Zhang, J, Ahmad, NS & Wang, S 2020, 'Convex Searches for Discrete-Time Zames-Falb Multipliers', IEEE Transactions on Automatic Control, vol. 65, no. 11, pp. 4538-4553. https://doi.org/10.1109/tac.2019.2958848

APA

Carrasco, J., Heath, W. P., Zhang, J., Ahmad, N. S., & Wang, S. (2020). Convex Searches for Discrete-Time Zames-Falb Multipliers. IEEE Transactions on Automatic Control, 65(11), 4538-4553. https://doi.org/10.1109/tac.2019.2958848

CBE

Carrasco J, Heath WP, Zhang J, Ahmad NS, Wang S. 2020. Convex Searches for Discrete-Time Zames-Falb Multipliers. IEEE Transactions on Automatic Control. 65(11):4538-4553. https://doi.org/10.1109/tac.2019.2958848

MLA

Carrasco, Joaquin et al. "Convex Searches for Discrete-Time Zames-Falb Multipliers". IEEE Transactions on Automatic Control. 2020, 65(11). 4538-4553. https://doi.org/10.1109/tac.2019.2958848

VancouverVancouver

Carrasco J, Heath WP, Zhang J, Ahmad NS, Wang S. Convex Searches for Discrete-Time Zames-Falb Multipliers. IEEE Transactions on Automatic Control. 2020 Nov 1;65(11):4538-4553. Epub 2019 Dec 10. doi: 10.1109/tac.2019.2958848

Author

Carrasco, Joaquin ; Heath, William P. ; Zhang, Jingfan et al. / Convex Searches for Discrete-Time Zames-Falb Multipliers. In: IEEE Transactions on Automatic Control. 2020 ; Vol. 65, No. 11. pp. 4538-4553.

RIS

TY - JOUR

T1 - Convex Searches for Discrete-Time Zames-Falb Multipliers

AU - Carrasco, Joaquin

AU - Heath, William P.

AU - Zhang, Jingfan

AU - Ahmad, Nur Syazreen

AU - Wang, Shuai

PY - 2020/11/1

Y1 - 2020/11/1

N2 - In this article, we develop and analyze convex searches for Zames-Falb multipliers. We present two different approaches: infinite impulse response (IIR) and finite impulse response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large-order FIR multiplier. We show that searches in discrete time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best ℓ 2 -stability results in the literature for slope-restricted nonlinearities. In particular, we establish the equivalence between the state-of-the-art Lyapunov results for slope-restricted nonlinearities and a subset of the FIR multipliers. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

AB - In this article, we develop and analyze convex searches for Zames-Falb multipliers. We present two different approaches: infinite impulse response (IIR) and finite impulse response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large-order FIR multiplier. We show that searches in discrete time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best ℓ 2 -stability results in the literature for slope-restricted nonlinearities. In particular, we establish the equivalence between the state-of-the-art Lyapunov results for slope-restricted nonlinearities and a subset of the FIR multipliers. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

U2 - 10.1109/tac.2019.2958848

DO - 10.1109/tac.2019.2958848

M3 - Erthygl

VL - 65

SP - 4538

EP - 4553

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 2334-3303

IS - 11

ER -