Finite-time behavior of inner systems

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

doi:10.1109/TAC.2003.814108

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 journal › Article › Academic › peer-review

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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 language	Undefined
Article number	10.1109/TAC.2003.814108
Pages (from-to)	1134-1149
Number of pages	16
Journal	IEEE transactions on automatic control
Volume	48
Issue number	7
DOIs	https://doi.org/10.1109/TAC.2003.814108
Publication status	Published - Jul 2003

Keywords

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

Access to Document

10.1109/TAC.2003.814108

Cite this

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title = "Finite-time behavior of inner systems",

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.",

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AU - Ludlage, Jobert H.A.

AU - Weiland, Siep

AU - Stoorvogel, Antonie Arij

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

PY - 2003/7

Y1 - 2003/7

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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

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KW - State-spacemethods

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JO - IEEE transactions on automatic control

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