Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Basic Numerical Methods and Software for Computer Aided Control f Design

  • Volker MehrmannEmail author
  • Paul Van Dooren
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_143


Basic principles for the development of computational methods for the analysis and design of linear time-invariant systems are discussed. These have been used in the design of the subroutine library SLICOT. The principles are illustrated on the basis of a method to check the controllability of a linear system.


Accuracy Basic numerical methods Benchmarking Controllability Documentation and implementation standards Efficiency Software design 
This is a preview of subscription content, log in to check access.


  1. 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/
  2. Benner P, Laub AJ, Mehrmann V (1997) Benchmarks for the numerical solution of algebraic Riccati equations. Control Syst Mag 17:18–28Google Scholar
  3. 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 1:499–532Google Scholar
  4. Demmel JW, Kågström B (1993) The generalized Schur decomposition of an arbitrary pencil Aλ B: robust software with error bounds and applications. Part I: theory and algorithms. ACM Trans Math Softw 19:160–174Google Scholar
  5. 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, KingstonGoogle Scholar
  6. Dongarra JJ, Du Croz J, Duff IS, Hammarling S (1990) A set of level 3 basic linear algebra subprograms. ACM Trans Math Softw 16:1–17Google Scholar
  7. 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 1–6Google Scholar
  8. Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  9. Gomez C, Bunks C, Chancelior J-P, Delebecque F (1997) Integrated scientific computing with scilab. Birkhäuser, Boston. https://www.scilab.org/
  10. Grübel G (1983) Die regelungstechnische Programmbibliothek RASP. Regelungstechnik 31: 75–81Google Scholar
  11. Luenberger DG (1967) Canonical forms for linear multivariable systems. IEEE Trans Autom Control 12(3):290–293MathSciNetGoogle Scholar
  12. Paige CC (1981) Properties of numerical algorithms related to computing controllability. IEEE Trans Autom Control AC-26:130–138MathSciNetGoogle Scholar
  13. Patel R, Laub A, Van Dooren P (eds) (1994) Numerical linear algebra techniques for systems and control. IEEE, PiscatawayGoogle Scholar
  14. The Control and Systems Library SLICOT (2012) The NICONET society. NICONET e.V. http://www.niconet-ev.info/en/
  15. The MathWorks, Inc. (2013) MATLAB version 8.1. The MathWorks, Inc., NatickGoogle Scholar
  16. The Numerical Algorithms Group (1993) NAG SLICOT library manual, release 2. The Numerical Algorithms Group, Wilkinson House, Oxford. Updates Release 1 of May 1990Google Scholar
  17. 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
  18. Van Dooren P (1981) The generalized eigenstructure problem in linear system theory. IEEE Trans Autom Control AC-26:111–129Google Scholar
  19. Varga A (ed) (2004) Special issue on numerical awareness in control. Control Syst Mag 24-1: 14–17Google Scholar
  20. 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, LundGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Institut für Mathematik MA 4-5Technische Universität BerlinBerlinGermany
  2. 2.ICTEAM: Department of Mathematical Engineering, Catholic University of LouvainLouvain-la-NeuveBelgium