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Robust Kalman filtering for uncertain discrete‐time linear systems
Author(s) -
Garcia Germain,
Tarbouriech Sophie,
Peres Pedro L. D.
Publication year - 2003
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.838
Subject(s) - kalman filter , estimator , control theory (sociology) , linear system , mathematics , norm (philosophy) , bounded function , robustness (evolution) , computer science , state (computer science) , mathematical optimization , algorithm , statistics , control (management) , mathematical analysis , biochemistry , chemistry , artificial intelligence , political science , law , gene
This paper presents a steady‐state robust state estimator for a class of uncertain discrete‐time linear systems with norm‐bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd.