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Basic Numerical Methods and Software for Computer-aided Control Systems Design

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Encyclopedia of Systems and Control

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Abstract

Basic numerical methods for the analysis and design of dynamical systems are at the heart of most techniques in systems and control theory that are used to describe, control, or optimize industrial and economical processes. There are many methods available for all the different tasks in systems and control, but even though most of these methods are based on sound theoretical principles, many of them still fail when applied to real-life problems. The reasons for this may be quite diverse, such as the fact that the system dimensions are very large, that the underlying problem is very sensitive to small changes in the data, or that the method lacks numerical robustness when implemented in a finite precision environment.

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References

  • Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Ostrouchov S, Sorensen D (1995) LAPACK users’ guide, 2nd edn. SIAM, Philadelphia. http://www.netlib.org/lapack/

  • Benner P, Laub AJ, Mehrmann V (1997) Benchmarks for the numerical solution of algebraic Riccati equations. Control Syst Mag 17:18–28

    Article  Google Scholar 

  • Benner P, Mehrmann V, Sima V, Van Huffel S, Varga A (1999) SLICOT-A subroutine library in systems and control theory. Appl Comput Control Signals Circuits 1:499–532

    Article  Google Scholar 

  • Demmel JW, Kågström B (1993) The generalized Schur decomposition of an arbitrary pencil A − λB: robust software with error bounds and applications. Part I: theory and algorithms. ACM Trans Math Softw 19:160–174

    Article  MATH  Google Scholar 

  • Denham MJ, Benson CJ (1981) Implementation and documentation standards for the software library in control engineering (SLICE). Technical report 81/3, Kingston Polytechnic, Control Systems Research Group, Kingston

    Google Scholar 

  • Dongarra JJ, Du Croz J, Duff IS, Hammarling S (1990) A set of level 3 basic linear algebra subprograms. ACM Trans Math Softw 16:1–17

    Article  MATH  Google Scholar 

  • Frederick DK (1988) Benchmark problems for computer aided control system design. In: Proceedings of the 4th IFAC symposium on computer-aided control systems design, Bejing, pp 1–6

    Google Scholar 

  • Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, Baltimore

    MATH  Google Scholar 

  • Gomez C, Bunks C, Chancelior J-P, Delebecque F (1997) Integrated scientific computing with scilab. Birkhäuser, Boston. https://www.scilab.org/

  • Grübel G (1983) Die regelungstechnische Programmbibliothek RASP. Regelungstechnik 31: 75–81

    MATH  Google Scholar 

  • Luenberger DG (1967) Canonical forms for linear multivariable systems. IEEE Trans Autom Control 12(3):290–293

    Article  MathSciNet  Google Scholar 

  • Paige CC (1981) Properties of numerical algorithms related to computing controllability. IEEE Trans Autom Control AC-26:130–138

    Article  MathSciNet  Google Scholar 

  • Patel R, Laub A, Van Dooren P (eds) (1994) Numerical linear algebra techniques for systems and control. IEEE, Piscataway

    MATH  Google Scholar 

  • The Control and Systems Library SLICOT (2012) The NICONET society. NICONET e.V. http://www.niconet-ev.info/en/

  • The MathWorks, Inc. (2013) MATLAB version 8.1. The MathWorks, Inc., Natick

    Google Scholar 

  • The Numerical Algorithms Group (1993) NAG SLICOT library manual, release 2. The Numerical Algorithms Group, Wilkinson House, Oxford. Updates Release 1 of May 1990

    Google Scholar 

  • The Working Group on Software (1996) SLICOT implementation and documentation standards 2.1. WGS-report 96-1. http://www.icm.tu-bs.de/NICONET/reports.html

  • Van Dooren P (1981) The generalized eigenstructure problem in linear system theory. IEEE Trans Autom Control AC-26:111–129

    Article  Google Scholar 

  • Varga A (ed) (2004) Special issue on numerical awareness in control. Control Syst Mag 24-1: 14–17

    Google Scholar 

  • Wieslander J (1977) Scandinavian control library. A subroutine library in the field of automatic control. Technical report, Department of Automatic Control, Lund Institute of Technology, Lund

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik MA 4-5, Technische Universität Berlin, Berlin, Germany

    Dr. Volker Mehrmann

  2. ICTEAM: Department of Mathematical Engineering, Catholic University of Louvain, Batiment Euler, Avenue Georges Lemaitre 4, Louvain-la-Neuve, Belgium

    Dr. Paul Van Dooren

Authors
  1. Dr. Volker Mehrmann
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  2. Dr. Paul Van Dooren
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Corresponding authors

Correspondence to Volker Mehrmann or Paul Van Dooren .

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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© 2013 Springer-Verlag London

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Mehrmann, V., Dooren, P.V. (2013). Basic Numerical Methods and Software for Computer-aided Control Systems Design. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_143-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_143-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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