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Keywords:
polynomial equation; Sylvester matrix; dynamical system
polynomial equation; Sylvester matrix; dynamical system
Summary:
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
References:
[1] Barmish B. R.: New Tools for Robustness of Linear Systems. MacMillan, New York 1994 Zbl 1094.93517
[2] Bose N. K., Shi Y. Q.: A simple general proof of Kharitonov’s generalized stability criterion. IEEE Trans. Circuits and Systems 34 (1987), 1233–1237 DOI 10.1109/TCS.1987.1086055 | MR 0908562 | Zbl 0643.93057
[3] Golub G. H., Loan C. F. Van: Matrix Computations. Third edition. Johns Hopkins University Press, Baltimore, Maryland 1996 MR 1417720
[4] Henrion D., Šebek M.: An efficient numerical method for the discrete-time symmetric matrix polynomial equation. IEE Proceedings, Control Theory and Applications 145 (1998), 5, 443–448
[5] Henrion D.: Reliable Algorithms for Polynomial Matrices. Ph. D. Thesis, Control Theory Department, Institute of Information Theory and Automation, Prague 1998
[6] Henrion D., Šebek M.: Symmetric matrix polynomial equation: Interpolation results. Automatica 34 (1998), 7, 811–824 DOI 10.1016/S0005-1098(98)00029-6 | MR 1635080 | Zbl 0935.65042
[7] Henrion D., Šebek M.: Reliable numerical methods for polynomial matrix triangularization. IEEE Trans. Automat. Control 44 (1999), 3, 497–508 DOI 10.1109/9.751344 | MR 1680274 | Zbl 0956.65036
[8] Higham N. J.: Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia 1996 MR 1368629 | Zbl 1011.65010
[9] Ježek J.: Conjugated and symmetric polynomial equations. Part II: Discrete-time systems. Kybernetika 19 (1983), 3, 196–211 MR 0716649 | Zbl 0556.93044
[10] Ježek J., Kučera V.: Efficient algorithm for matrix spectral factorization. Automatica 21 (1985), 6, 663–669 DOI 10.1016/0005-1098(85)90040-8 | MR 0818806
[11] Ježek J.: Symmetric matrix polynomial equations. Kybernetika 22 (1986), 1, 19–30 MR 0839342 | Zbl 0599.93008
[12] Ježek J., Hunt K. J.: Coupled polynomial equations of LQ control synthesis and an algorithm for solution. Internat. J. Control 58 (1993), 5, 1155–1167 DOI 10.1080/00207179308923047 | MR 1242443
[13] Kailath T.: Linear Systems. Prentice Hall, Englewood Cliffs, N.J. 1980 MR 0569473 | Zbl 0870.93013
[14] Kučera V.: Discrete Linear Control: The Polynomial Approach. Wiley, Chichester 1979 MR 0573447
[15] Kučera V.: Analysis and Design of Discrete Linear Control Systems. Prentice Hall, London 1991 MR 1182311 | Zbl 0762.93060
[16] Lindbom L.: A Wiener Filtering Approach to the Design of Tracking Algorithms with Applications to Mobile Radio Communications. Ph. D. Thesis, Signal Processing Group, Department of Technology, Uppsala University, Sweden 1995
[17] MacChi O.: Adaptive Processing: the Least Mean Squares Approach and Applications in Transmission. Wiley, Chichester 1995
[18] Proakis J. G., Salehi M.: Communication Systems Engineering. Prentice Hall, Englewood Cliffs, N.J. 1994 Zbl 0864.94001
[19] Šebek M., Kwakernaak H., Henrion, D., Pejchová S.: Recent Progress in Polynomial Methods and Polynomial Toolbox for Matlab Version 2. 0. In: Proc. Conference on Decision and Control, IEEE, Tampa 1998, pp. 3661–3668.See also the web page www.polyx.com
[20] Söderström T., Ježek, J., Kučera V.: An efficient and versatile algorithm for computing the covariance function of an ARMA process. IEEE Trans. Signal Processing 46 (1998), 6, 1591–1600 DOI 10.1109/78.678473 | MR 1667256 | Zbl 1028.93031
[21] Willems J. C., Trentelman H. L.: On quadratic differential forms. SIAM J. Control Optim. 36 (1998), 5, 1703–1749 DOI 10.1137/S0363012996303062 | MR 1626821 | Zbl 0912.93006
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