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Partial Stabilization of Descriptor Systems Using Spectral Projectors

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Numerical Linear Algebra in Signals, Systems and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 80))

Abstract

We consider the stabilization problem for large-scale linear descriptor systems in continuous- and discrete-time. We suggest a partial stabilization algorithm which preserves stable poles of the system while the unstable ones are moved to the left half plane using state feedback. Our algorithm involves the matrix pencil disk function method to separate the finite from the infinite generalized eigenvalues and the stable from the unstable eigenvalues. In order to stabilize the unstable poles, either the generalized Bass algorithm or an algebraic Bernoulli equation can be used. Some numerical examples demonstrate the behavior of our algorithm.

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Notes

  1. 1.

    Available Version: 1.05, 1 October 2005.

  2. 2.

    See http://www.pscom.uji.es/plic.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Peter Benner

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  1. Peter Benner
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Correspondence to Peter Benner .

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Editors and Affiliations

  1. CESAME, Batiment Euler, Universite Catholique de Louvain, 4, avenue Georges Lemaitre, Louvain la Neuve, 1348, Belgium

    Paul Van Dooren

  2. Department of Electrical and Computer, Engineering, Texas A&M University, Zachry Engineering Center, College Station, 77843-3128, Texas, USA

    Shankar P. Bhattacharyya

  3. Dept. Mathematics, Chinese University Hong Kong, Shatin, New Territories, Hong Kong/PR China

    Raymond H. Chan

  4. Dept. Mathematics, University of Connecticut, Auditorium Road 196, Storrs, 06269-3009, Connecticut, USA

    Vadim Olshevsky

  5. , Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    Aurobinda Routray

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Benner, P. (2011). Partial Stabilization of Descriptor Systems Using Spectral Projectors. In: Van Dooren, P., Bhattacharyya, S., Chan, R., Olshevsky, V., Routray, A. (eds) Numerical Linear Algebra in Signals, Systems and Control. Lecture Notes in Electrical Engineering, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0602-6_3

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  • DOI: https://doi.org/10.1007/978-94-007-0602-6_3

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0601-9

  • Online ISBN: 978-94-007-0602-6

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