Computer Aided Control System Design
  Polynomial Control Design Methods

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home news glossary groups people positions problems publications software benchmarks courses conferences This webpage aims at collecting references that are relevant for polynomial methods and especially for numerical computation with polynomial matrices.

Books

Control design methods - general

  • Antsaklis, P.J., Michel, A.N.Linear Systems. McGraw-Hill, 1997.
  • Kailath, T. Linear Systems. Prentice Hall, 1980.
  • Kucera, V. Discrete Linear Control - The Polynomial Equation Approach. John Wiley and Sons Ltd., 1979.
  • Grimble, M. J., Kucera, V. Polynomial Methods for Control Systems Design, Springer-Verlag, 1996.
  • Hunt, K. (Ed.) Polynomial Methods in Optimal Control and Filtering, Peter Peregrinus, Ltd., 1993.
  • Polderman, J.W., Willems, J.C. Introduction to Mathematical Systems Theory. Springer-Verlag New York, 1998.
  • Vardulakis, A.I.G. Linear Multivariable Control. Algebraic Analysis and Synthesis Methods, J. Wiley and Sons Ltd., Chichester, England, 1991.
  • Vidyasagar, M. Control Systems Synthesis: A Factorization Approach. MIT Press, 1985.

Mathematics for polynomials and polynomial matrices - general

  • Ball, J.A., Gohberg, I., Rodman, L. Interpolation of Rational Matrix Functions. Birkhauser Verlag Basel, 1990.
  • Barnett, S. Polynomials and Linear Control Systems. Marcel Dekker, Inc., 1983.
  • Fuhrmann, P. A. A Polynomial Approach to Linear Algebra. Springer-Verlag New York, Inc., 1996.
  • Gohberg, I., Lancaster, B., Rodman, L. Matrix Polynomials. Academic Press, 1982.

Numerical methods for polynomials and polynomial matrices

  • Stefanidis, P., Paplinski, A.P., Gibbard, M.J. Numerical Operations with Polynomial Matrices. Springer-Verlag Berlin Heidelberg, 1992.
  • Pan, V.Y. Structured Matrices and Polynomials. Birkhauser Boston, 2001.

Research papers in journals and conferences

H2 optimal control

Hinf optimal control

l1 optimal control

Model predictive control

Spectral factorization of rational and polynomial matrices

  • Vosty, Z. New algoritgm for polynomial spectral factorization with quadratic convergence I. Kybernetika, Vol. 11, No. 6, 1975, pp. 415-422.
  • Vosty, Z. New algoritgm for polynomial spectral factorization with quadratic convergence II. Kybernetika, Vol. 12, No. 4, 1976, pp. 248-259.
  • Callier, F. On polynomial matrix spectral factorization by symmetric extraction. IEEE Transactions on Automatic Control, Vol. 30, No. 5, May 1985, pp. 453-464.
  • Jezek, J., Kucera, V. Efficient algorithm for matrix spectral factorization. Automatica, Vol. 21, No. 6, pp. 663-669.

Linear equations with rational and polynomial matrices

  • Jezek, J. New algorithm for minimal solution of linear polynomial equations. Kybernetika, Vol. 18, pp. 505-516, 1982.
  • Jezek, J. Conjugated and symmetric polynomial equations. Part I: Continuous-time systems. Kybernetika, Vol. 19, No. 2, 1983.
  • Jezek, J. Conjugated and symmetric polynomial equations. Part II: Discrete-time systems. Kybernetika, Vol. 19, No. 3, 1983.
  • Kucera, V. Diophantine equations in control - a survey. Automatica, Vol. 29, No. 6, pp. 1361-1395, 1993.

Numerical algorithms for structured matrices, especially (block) Toeplitz matrices

Industrial applications of polynomial methods