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 -