Abstract
The paper deals with the local sensitivity analysis of the discrete-time infinite-horizon H 2 estimation problem. An improved, nonlinear sensitivity estimate is derived which is less conservative than the existing, condition number based sensitivity estimates.
This work is supported by the European Union under Grants 15010/02Y0064/03-04 CAR/Presage No 4605 Obj. 2-2004:2 – 4.1 No 160/4605.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Hassibi, B., Sayed, A.H., Kailath, T.: Indefinite-Quadratic Estimation and Control: A Unified Approach to H2 and H? ∞ ? Theories. SIAM, Philadelphia (1999)
Konstantinov, M.M., Petkov, P.H., Christov, N.D., Gu, D.W., Mehrmann, V.: Sensitivity of Lyapunov equations. In: Mastorakis, N. (ed.) Advances in Intelligent Systems and Computer Science, pp. 289–292. WSES Press, N.Y (1999)
Konstantinov, M.M., Petkov, P.H., Gu, D.W.: Improved perturbation bounds for general quadratic matrix equations. Numer. Func. Anal. and Optimiz. 20, 717–736 (1999)
Christov, N.D., Lesecq, S., Konstantinov, M.M., Petkov, P.H., Barraud, A.: New perturbation bounds for Sylvester equations. In: Proc. 39th IEEE Conf. on Decision and Control, Sydney, December 12-15, pp. 4233–4234 (2000)
Christov, N.D., Najim, M., Grivel, E., Henry, D.: On the local sensitivity of the discrete-time H ∞ estimation problem. In: Proc. 15th IFAC World Congress, Barcelona, July 21-26 (2002) paper T-Tu-A01/1091
Konstantinov, M.M., Petkov, P.H., Christov, N.D.: Perturbation analysis of the continuous and discrete matrix Riccati equations. In: Proc. 1986 American Control Conf., Seattle, June 18-20, vol. 1, pp. 636–639 (1986)
Gahinet, P., Laub, A.J.: Computable bounds for the sensitivity of the algebraic Riccati equation. SIAM J. Contr. Optim. 28, 1461–1480 (1990)
Petkov, P.H., Christov, N.D., Konstantinov, M.M.: Computational Methods for Linear Control Systems. Prentice-Hall, N.Y (1991)
Konstantinov, M.M., Petkov, P.H., Christov, N.D.: Perturbation analysis of the discrete Riccati equation. Kybernetika 29, 18–29 (1993)
Ghavimi, A.R., Laub, A.J.: Backward error, sensitivity and refinement of computed solutions of algebraic Riccati equations. Numer. Lin. Alg. Appl. 2, 29–49 (1995)
Sun, J.-G.: Perturbation theory for algebraic Riccati equations. SIAM J. Matrix Anal. Appl. 19, 39–65 (1998)
Sun, J.-G.: Condition numbers of algebraic Riccati equations in the Frobenius norm. Lin. Alg. Appl. 350, 237–261 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Christov, N.D., Najim, M., Grivel, E. (2006). Improved Sensitivity Estimate for the H 2 Estimation Problem . In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_93
Download citation
DOI: https://doi.org/10.1007/11758501_93
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34379-0
Online ISBN: 978-3-540-34380-6
eBook Packages: Computer ScienceComputer Science (R0)