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Some Inverse Eigenvalue and Pole Placement Problems for Linear and Quadratic Pencils

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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))

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Abstract

Differential equation models for vibrating systems are associated with matrix eigenvalue problems. Frequently the undamped models lead to problems of the generalized eigenvalue type and damped models lead to problems of the quadratic eigenvalue type. The matrices in these systems are typically real and symmetric and are quite highly structured. The design and stabilisation of systems modelled by these equations (eg., undamped and damped vibrating systems) requires the determination of solutions to the inverse eigenvalue problems which are themselves real, symmetric and possibly have some other structural properties. In this talk we consider some pole assignment problems and inverse spectral problems for generalized and quadratic symmetric pencils, discuss some advances and point to some work that remains to be done.

Dedicated with friendship and respect to Biswa N. Datta for his contributions to mathematics. S. Elhay 2008

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Notes

  1. 1.

    In this paper a conjugate transpose is denoted by a superscript H while transposition, which is denoted by a superscript T, does not mean conjugate transpose even for complex quantities.

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Authors and Affiliations

  1. School of Computer Science, University of Adelaide, Adelaide, SA, 5005, Australia

    Sylvan Elhay

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  1. Sylvan Elhay
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Correspondence to Sylvan Elhay .

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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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Elhay, S. (2011). Some Inverse Eigenvalue and Pole Placement Problems for Linear and Quadratic Pencils. 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_12

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  • DOI: https://doi.org/10.1007/978-94-007-0602-6_12

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