Strong stability of a coupled system composed of impedance-passive linear systems which may both have imaginary eigenvalues

Xiaowei Zhao, George Weiss

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

Abstract

We consider coupled systems consisting of a well-posed and impedance passive linear system (that may be infinite dimensional), with semigroup generator A and transfer function G, and an internal model controller (IMC), connected in feedback. The IMC is finite dimensional, minimal and impedance passive, and it is tuned to a finite set of known disturbance frequencies ωj, where j E {1,⋯ n }, which means that its transfer function g has poles at the points iωj. We also assume that g has a feedthrough term d with Re d > 0. We assume that Re G(iωj) > 0 for all j {1,⋯ n} and the points iωj are not eigenvalues of A. We can show that the closed-loop system is well-posed and input-output stable (in particular, (I + gG)-1 E H and also G(1 + gG)-l E H ). It is also easily seen that the closed-loop system is impedance passive. We show that if A has at most a countable set of imaginary eigenvalues, that are all observable, and A has no other imaginary spectrum, then the closed-loop system is strongly stable. This result is illustrated with a wind turbine tower model controlled by an IMC.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages521-526
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - 2 Jul 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Country/TerritoryUnited States
CityMiami
Period17/12/1819/12/18

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Control and Systems Engineering
  • Modelling and Simulation

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