Abstract
The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H ∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H ∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Savkin and I. R. Petersen, Fixed-order robust filtering for linear uncertain systems, in Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, 1996, 4800–4801.
L. Xie and C. E. de Souza, On Robust filtering for linear systems with parameter uncertainty, in Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans La, 1995, 2087–2092.
T. H. Lee, W. S. Ra, T. S. Yoon, J. B. Park, S. Y. Jung, and J. E. Seo, Robust filtering for linear discrete-time systems with parameter uncertainties: A Krein space estimation approach, in Proceedings of the 42nd IEEE Conference on Decision and Control, Hawii, USA, 2003, 1285–1290.
H. Z. Li and M. Y. Fu, An LMI approach to Robust H ∞ filtering for linear systems, in Proceedings of the 34th Conference on Decision and Control, New Orleans La, 1995, 3608–3613.
Y. S. Lin, J. X. Qian, and S. L. Xu, A LMI approach to robust H ∞ filtering for discrete-time systems, in Proceedings of IEEE Conference on Control Application, 2003, 230–233.
M. C.de Oliveira, J. Bernussou and J. C. Geromel, A new discrete-time robust stability condition, System & Control Letter, 1999, 37(4):261–265.
R. M. Palhares and P. L. D. Peres, Robust filter design with pole constraints for discrete-time systems, Journal of the Franklin Institute, 2000, 337(6): 713–723.
L. H. Xie, L. L. Hu, D. Zhang, and H. S. Zhang, Robust filtering for uncertain discrete-time: An improved LMI approach, in Proceedings of the 42nd IEEE Conference on Decision and Control, Hawali, USA, 2003, 906–911.
H. J. Gao and C. H. Wang, New approaches to Robust and filtering for uncertain discrete-time systems, Science In China (Series F), 2003, 46(5): 356–370.
J. C. Geromel, Optimal linear filtering under parameter uncertainty, IEEE Trans.on Signal Processing, 1999, 47(1): 168–175.
R. M. Palhares and P. L. D. Peres, Robust H ∞ filtering design with pole placement constraint via linear matrix inequality, J. of Optimization Theory and Application, 1999, 102(2): 239–261.
H. J. Gao and C. H. Wang, Robust state estimation for systems with uncertain parameters (in Chinese), Control and Decision, 2004, 19(2): 147–152.
M. C. De Oliveira, J. C. Geromel, and J. Bernussou, An LMI optimization approach to multiobjective controller design for discrete-time systems, in Proceedings of the 38th Conference on Decision and Control, Phoenix, USA, 1999, 3611–3616.
P. J. de Oliveira, R. C. F. Oliveira, V. J. S. Leite, V. F. Montagner, and P. L. D. Peres, Hinf guaranteed cost computation by means of parameter-dependent Lyapunov functions, Automatica, 2004, 40(6): 1053–1061.
U. Shaked, Improved LMI representations for analysis and the design of continuous-time systems with polytopic type uncertainty, IEEE Transactions on Automatic Control, 2001, 46(4): 652–656.
T. Li and Y. Jia, Improved LMI presentations for bounded real criterion of systems with polytopic type uncertainty, in Proceedings of the American Conference, Denver, Colorado, 2000, 851–856.
A.G. Wu and G. R. Duan, Robust H-infinity estimation for continuous-time polytopic uncertain systems, Journal of Control Theory and Applications, 2005, 3(4): 393–398.
Author information
Authors and Affiliations
Corresponding author
Additional information
The research is supported by the National Natural Science Foundation of China under Grant No. 60374024 and by Program for Changjiang Scholars and Innovative Research Teams in University.
Rights and permissions
About this article
Cite this article
Wu, A., Dong, H. & Duan, G. Improved Robust H-Infinity Estimation for Uncertain Continuous-Time Systems. Jrl Syst Sci & Complex 20, 362–369 (2007). https://doi.org/10.1007/s11424-007-9031-4
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11424-007-9031-4