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Improved perturbation bounds for general quadratic matrix equations. (English) Zbl 0937.15009

This paper deals with the perturbation analysis of general algebraic quadratic matrix equations. As special cases, algebraic matrix Riccati equations are treated which arise in the optimal control and filtering of continuous, time-invariant linear systems. The authors obtain perturbation bounds which improve the most general ones known so far [cf. M. M. Konstantinov, P. Hr. Petkov, and N. D. Christov, SIAM J. Sci. Stat. Comput. 11, No. 6, 1159-1163 (1990; Zbl 0716.15013)]. The main tools are Lyapunov majorants, fixed point principles, and estimations of the norm of tensor products of matrices.

MSC:

15A24 Matrix equations and identities
93B35 Sensitivity (robustness)
93C73 Perturbations in control/observation systems

Citations:

Zbl 0716.15013

Software:

DMSRIC; DGRSVX
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Full Text: DOI

References:

[1] Grebenikov E. A., Constructive Methods for Analysis of Nonlinear Systems. (1979) · Zbl 0466.65041
[2] Kantorovich L., Functional Analysis in Normed Spaces. (1977) · Zbl 0127.06102
[3] Kenney C., SIAM J. Cont. Optim. 28 pp 50– (1990) · Zbl 0695.65025 · doi:10.1137/0328003
[4] Konstantinov, M., Petkov, P., Gu, D. W. and Postlethwaite, I. Feb 1995. ”Perturbation techniques for linear control problems”. Feb, Leicester, UK: Department of Engineering, Leicester University. Technical Report 95-7
[5] Konstantinov, M., Petkov, P., Gu, D. W. and Postlethwaite, I. June 1996. ”Perturbation analysis in finite dimensional spaces”. June, Leicester, UK: Department of Engineering, Leicester University. · Zbl 0923.93006
[6] Konstantinov, M. M., Petkov, P.Hr. and Christov, N. D. 1986. Perturbation analysis of the continuous and discrete matrix Riccati equations. Proc. 1986 American Control Conference. June1986., Seattle, WA. pp.636–639.
[7] Konstantinov M. M., SIAM J. Sci. Statist. Comput. 11 pp 1159– (1990) · Zbl 0716.15013 · doi:10.1137/0911065
[8] Ortega J., Iterative Solution of Nonlinear Equations in Several Variables. (1970) · Zbl 0241.65046
[9] Petkov, P.Hr., Konstantinov, M. M. and Mehrmann, V. May 1998. ”DGRSVX and DMSRIC: Fortran 77 subroutines for solving continuous-time matrix algebraic Riccati equations with condition and accuracy estimates”. May, Chemnitz, Germany: Fakultat fur Mathematik. Technical Report SFB393/98-16
[10] Rice J. R., SIAM J. Numer. Anal 3 pp 287– (1966) · Zbl 0143.37101 · doi:10.1137/0703023
[11] Shayman M. A., SIAM J. Cont Optim. 21 pp 375– (1983) · doi:10.1137/0321021
[12] Shayman M. A., SIAM J. Cont. Optim. 21 pp 395– (1983) · Zbl 0537.93023 · doi:10.1137/0321022
[13] Sun J. -G., SIAM J. Matrix Anal. Appl. 19 pp 39– (1998) · Zbl 0914.15009 · doi:10.1137/S0895479895291303
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