Finite-time behavior of inner systems

Jobert H.A. Ludlage, Siep Weiland, Antonie Arij Stoorvogel, Ton A.C.P.M. Backx

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller.
Original languageUndefined
Article number10.1109/TAC.2003.814108
Pages (from-to)1134-1149
Number of pages16
JournalIEEE transactions on automatic control
Volume48
Issue number7
DOIs
Publication statusPublished - Jul 2003

Keywords

  • EWI-16631
  • Tracking
  • Stability
  • Control Systems
  • Optimal Control
  • IR-68907
  • State-spacemethods

Cite this

Ludlage, J. H. A., Weiland, S., Stoorvogel, A. A., & Backx, T. A. C. P. M. (2003). Finite-time behavior of inner systems. IEEE transactions on automatic control, 48(7), 1134-1149. [10.1109/TAC.2003.814108]. https://doi.org/10.1109/TAC.2003.814108
Ludlage, Jobert H.A. ; Weiland, Siep ; Stoorvogel, Antonie Arij ; Backx, Ton A.C.P.M. / Finite-time behavior of inner systems. In: IEEE transactions on automatic control. 2003 ; Vol. 48, No. 7. pp. 1134-1149.
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Ludlage, JHA, Weiland, S, Stoorvogel, AA & Backx, TACPM 2003, 'Finite-time behavior of inner systems' IEEE transactions on automatic control, vol. 48, no. 7, 10.1109/TAC.2003.814108, pp. 1134-1149. https://doi.org/10.1109/TAC.2003.814108

Finite-time behavior of inner systems. / Ludlage, Jobert H.A.; Weiland, Siep; Stoorvogel, Antonie Arij; Backx, Ton A.C.P.M.

In: IEEE transactions on automatic control, Vol. 48, No. 7, 10.1109/TAC.2003.814108, 07.2003, p. 1134-1149.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Finite-time behavior of inner systems

AU - Ludlage, Jobert H.A.

AU - Weiland, Siep

AU - Stoorvogel, Antonie Arij

AU - Backx, Ton A.C.P.M.

PY - 2003/7

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N2 - In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller.

AB - In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller.

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KW - Tracking

KW - Stability

KW - Control Systems

KW - Optimal Control

KW - IR-68907

KW - State-spacemethods

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DO - 10.1109/TAC.2003.814108

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Ludlage JHA, Weiland S, Stoorvogel AA, Backx TACPM. Finite-time behavior of inner systems. IEEE transactions on automatic control. 2003 Jul;48(7):1134-1149. 10.1109/TAC.2003.814108. https://doi.org/10.1109/TAC.2003.814108