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Encyclopedia of Systems and Control pp 1–11Cite as

Spectral Factorization

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Abstract

For more than half a century, spectral factorization is encountered in various fields of science and engineering. It is a useful tool in robust and optimal control and filtering and many other areas. It is also a nice control-theoretical concept closely related to Riccati equation. As a quadratic equation in polynomials, it is a challenging algebraic task.

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Bibliography

  • Callier FM (1985) On polynomial matrix spectral factorization by symmetric extraction. IEEE Trans Autom Control 30:453–464

    Article  MathSciNet  Google Scholar 

  • Callier FM, Desoer CA (1982) Multivariable feedback systems. Springer, New York

    Book  Google Scholar 

  • Davis MC (1963) Factorising the spectral matrix. IEEE Trans Autom Control 8:296

    Article  Google Scholar 

  • Green M, Glover K, Limebeer DJN, Doyle J (1990) A J-spectral factorization approach to H-infinity control. SIAM J Control Opt 28:1350–1371

    Article  MathSciNet  Google Scholar 

  • Henrion D, Sebek M (2000) An algorithm for polynomial matrix factor extraction. Int J Control 73(8):686–695

    Article  MathSciNet  Google Scholar 

  • Henrion D, Šebek M, Kučera V (2003) Positive polynomials and robust stabilization with fixed-order controllers. IEEE Trans Autom Control 48:1178–1186

    Article  Google Scholar 

  • Hromčík M, Šebek M (2007) Numerical algorithms for polynomial Plus/Minus factorization. Int J Robust Nonlinear Control 17(8):786–802

    Article  Google Scholar 

  • Jakubovič VA (1970) Factorization of symmetric matrix polynomials. Dokl Akad Nauk SSSR 194(3):532–535

    MathSciNet  Google Scholar 

  • Ježek J, Kučera V (1985) Efficient algorithm for matrix spectral factorization. Automatica 29:663–669

    Google Scholar 

  • Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Kučera V (1979) Discrete linear control: the polynomial equation approach. Wiley, Chichester

    Google Scholar 

  • Kučera V (2007) Polynomial control: past, present, and future. Int J Robust Nonlinear Control 17:682–705

    Article  Google Scholar 

  • Kwakernaak H (1991) The polynomial approach to a H-optimal regulation. In: Mosca E, Pandolfi L (eds) H-infinity control theory. Lecture notes in maths, vol 1496. Springer, Berlin

    Google Scholar 

  • Kwakernaak H, Šebek M (1994) Polynomial J-spectral factorization. IEEE Trans Autom Control 39:315–328

    Article  Google Scholar 

  • Oara C, Varga A (2000) Computation of general inner-outer and spectral factorizations. IEEE Trans Autom Control 45:2307–2325

    Article  MathSciNet  Google Scholar 

  • Sayed AH, Kailath T (2001) A survey of spectral factorization methods. Numer Linear Algebra Appl 8(6–7):467–496

    Article  MathSciNet  Google Scholar 

  • Šebek M (1992) J-spectral factorization via Riccati equation. In: Proceedings of the 31st IEEE CDC, Tuscon, pp 3600–3603

    Google Scholar 

  • Sternad M, Ahlén A (1993) Robust filtering and feedforward control based on probabilistic descriptions of model errors. Automatica 29(3):661–679

    Article  MathSciNet  Google Scholar 

  • Vostrý Z (1975) New algorithm for polynomial spectral factorization with quadratic convergence. Kybernetika 11:415, 248

    Google Scholar 

  • Wiener N (1949) Extrapolation, interpolation and smoothing of stationary time series. Wiley, New York

    Google Scholar 

  • Wilson GT (1972) The factorization of matricial spectral densities. SIAM J Appl Math 23:420

    Article  MathSciNet  Google Scholar 

  • Youla DC, Kazanjian NN (1978) Bauer-type factorization of positive matrices and the theory of matrix polynomials orthogonal on the unit circle. IEEE Trans Circuits Syst 25:57

    Article  MathSciNet  Google Scholar 

  • Zhong QC (2005) J-spectral factorization of regular para-Hermitian transfer matrices. Automatica 41:1289–1293

    Article  Google Scholar 

  • Zhou K, Doyle JC (1998) Essentials of robust control. Prentice-Hall, Upper Saddle River

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering, Department of Control Engineering, Czech Technical University in Prague, Prague 6, Czech Republic

    Michael Šebek

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  1. Michael Šebek
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Corresponding author

Correspondence to Michael Šebek .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2015 Springer-Verlag London

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Šebek, M. (2015). Spectral Factorization. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_240-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_240-2

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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Chapter history

  1. Latest

    Spectral Factorization
    Published:
    05 May 2015

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_240-2

  2. Original

    Spectral Factorization
    Published:
    25 September 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_240-1

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