Abstract
This paper proposes an easier frequency domain solution to the standard H ∞ filtering problem using a polynomial approach. The design of the H ∞ filter in the frequency domain is first obtained from the time domain solution which is related to a Riccati equation, and then by the use of the connecting relationship between the time and frequency domain approach given by Hippe [8], its representation in the frequency domain is derived. The filter is easy to calculate as it requires the computation of a single gain and it is easily implementable also. A numerical example is given to illustrate the presented approach.
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Montassar Ezzine was born in 1979. He received his Electrical Engineering degree in 2004 and the master diploma in 2006 from the School of Engineers of Monastir — Tunisia (ENIM). He is currently a Ph.D. student in, Ecole Nationale d’Ingénieurs de Monastir (ENIM) and Centre de Recherche en Automatique de Nancy (CRAN, CNRS). His research interests are about Observation and observer based-control for linear systems in the time and frequency domains.
Harouna Souley Ali received his Ph.D. degree in Automatic Control from the Université Henri Poincaré of Nancy, France, in 2002. He is now an Associate Professor in Automatic Control at the Université Henri Poincaré (Nancy Université) and is with the Centre de Recherche en Automatique de Nancy (CRAN, CNRS). His current research topics are in the area of robust control and filtering of linear and nonlinear systems.
Mohamed Darouach received his “Docteur Ingénieur” and “Docteur d’Etat” degrees from the Université Henri Poincaré of Nancy I, France, in 1983 and 1986 respectively. He is currently with Université Henri Poincaré (Nancy Université) where he holds a position of Professor in Automatic Control and is a vice-director of the Centre de Recherche en Automatique de Nancy (CRAN, CNRS). His current research interests include observer theory and application, fault detection and robust control.
Hassani Messaoud has received his Bachelor’s degree in Electrical Engineering in 1983 and his Master of Science in Control Engineering 1985 from the High Normal School of Technical Education (ENSET) in Tunis — Tunisia. His Ph.D. in Control Engineering was prepared at the University of Nice — Sophia Antipolis/France in 1993 and his Habilitation Diploma was defended at the School of Engineers (ENIT) in Tunis -Tunisia. He is presently a Professor at the School of Engineers of Monastir — Tunisia (ENIM) and Director of the laboratory ATSI. His main interest is robustness in identification and control of non linear systems with application to diagnosis and equalization of numerical communication channels.
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Ezzine, M., Ali, H.S., Darouach, M. et al. Full order H ∞ filtering for linear systems in the frequency domain. Int. J. Control Autom. Syst. 9, 558–565 (2011). https://doi.org/10.1007/s12555-011-0316-y
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DOI: https://doi.org/10.1007/s12555-011-0316-y