TY - GEN

T1 - Strong stability of a coupled system composed of impedance-passive linear systems which may both have imaginary eigenvalues

AU - Zhao, Xiaowei

AU - Weiss, George

N1 - Publisher Copyright:
© 2018 IEEE.

PY - 2018/7/2

Y1 - 2018/7/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062180990&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619326

DO - 10.1109/CDC.2018.8619326

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AN - SCOPUS:85062180990

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 521

EP - 526

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -