zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Resilient linear filtering of uncertain systems. (English) Zbl 1162.93403
The objective of the paper is to contribute to the further development of resilient linear filtering for a class of continuous-time systems with norm-bounded uncertainties. The term “resilient” means robustness with respect to plant parametric uncertainties and against gain perturbations in filter matrices. A class of resilient linear filters with additive filter gain perturbations is described. The perturbations are supposed to be present in both the estimator gain and dynamic matrices. The design problem of robust resilient filtering is formulated as a problem of convex optimization over linear matrix inequalities (LMIs). An important special case with resilient linear filter and additive gain perturbations is considered, which recovers, in the nominal case, previously known filtering results. By a limiting approach, an LMI result on resilient Kalman filter is derived and finally, it is demonstrated that the case of multiplicative filter gain perturbations can be developed conveniently as an extension of the forgoing results. An example illustrates the theoretical developments.

93E11Filtering in stochastic control
93D09Robust stability of control systems
Full Text: DOI
[1] Bernstein, D. S.; Haddad, W. M.: Steady-state Kalman filtering with an H$\infty $error bound. Systems and control letters 16, 309-317 (1991)
[2] Dorato, P. (1998). Non-fragile controllers design: An overview. Proceedings of the American control conference, Philadelphia, PA (pp. 2829-2831).
[3] Doyle, J. C.; Stein, G.: Robustness with observers. IEEE transactions on automatic control 24, 607-611 (1979) · Zbl 0412.93030
[4] Fu, M.; De Souza, C. E.; Xie, L.: H\infty-estimation for uncertain systems. International journal of robust and nonlinear control 2, 87-105 (1992) · Zbl 0765.93032
[5] Gahinet, P.; Apkarian, P.: A linear matrix inequality approach to H$\infty $control. International journal of robust and nonlinear control 4, 421-448 (1994) · Zbl 0808.93024
[6] Geromel, J. C.: Optimal linear filtering with parameter uncertainty. IEEE transactions on signal processing 47, 168-175 (1999) · Zbl 0988.93082
[7] Haddad, W. M., & Corrado, J. R. (1998). Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations. Proceedings of the American control conference, Philadelphia, PA (pp. 2837-2841).
[8] Keel, L. H.; Bhattacharyya, S. P.: Robust, fragile, or optimal?. IEEE transactions on automatic control 42, 1098-1105 (1997) · Zbl 0900.93075
[9] Mahmoud, M. S.: Robust control and filtering for time-delay systems. (2000) · Zbl 0969.93002
[10] Nagpal, K. M.; Khargonekar, P. P.: Filtering and smoothing in H$\infty $setting. IEEE transactions on automatic control 36, 152-166 (1991) · Zbl 0758.93074
[11] Scherer, C.; Gahinet, P.; Chilali, M.: Multiobjective output-feedback control via LMI optimization. IEEE transactions on automatic control 42, 896-911 (1997) · Zbl 0883.93024
[12] Shaked, U.; De Souza, C. E.: Robust minimum variance filtering. IEEE transactions on signal processing 43, 2474-2483 (1995)
[13] Yang, G. H.; Wang, J. L.: Robust resilient Kalman filtering for uncertain linear systems with estimator gain uncertainty. IEEE transactions on automatic control 46, 343-348 (2001) · Zbl 1056.93635