Kalman conjecture for resonant second-order systems with time delay

Jingfan Zhang; William Heath; Joaquin  Carrasco

doi:10.1109/cdc.2018.8619845

Kalman conjecture for resonant second-order systems with time delay

Jingfan Zhang, William Heath, Joaquin Carrasco

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

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Abstract

We construct Zames-Falb multipliers for secondorder systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.

Original language	English
Title of host publication	57th IEEE Conference on Decision and Control 2018
DOIs	https://doi.org/10.1109/cdc.2018.8619845
Publication status	Published - 2019

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CDC18_0766_FIAccepted author manuscript, 423 KB

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title = "Kalman conjecture for resonant second-order systems with time delay",

abstract = "We construct Zames-Falb multipliers for secondorder systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.",

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AU - Zhang, Jingfan

AU - Heath, William

AU - Carrasco, Joaquin

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N2 - We construct Zames-Falb multipliers for secondorder systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.

AB - We construct Zames-Falb multipliers for secondorder systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.

U2 - 10.1109/cdc.2018.8619845

DO - 10.1109/cdc.2018.8619845

M3 - Conference contribution

BT - 57th IEEE Conference on Decision and Control 2018

ER -

Kalman conjecture for resonant second-order systems with time delay

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