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Full Order H∞ Filter Design for Delayed Singular Systems with Unknown Input and Bounded Disturbance: Time and Frequency Domain Approaches

Malek Khadhraoui(1*), Montassar Ezzine(2), Hassani Messaoud(3), Mohamed Darouach(4)

(1) Laboratoire de recherche LARATSI, Ecole Nationale d'Ingénieurs de Monastir (ENIM), Université de Monastir Avenue Ibn El Jazzar, Tunisia
(2) Laboratoire de recherche LARATSI, Ecole Nationale d'Ingénieurs de Monastir (ENIM), Université de Monastir Avenue Ibn El Jazzar, Tunisia
(3) Laboratoire de recherche LARATSI, Ecole Nationale d'Ingénieurs de Monastir (ENIM), Université de Monastir Avenue Ibn El Jazzar, Tunisia
(4) Centre de Recherche en Automatique de Nancy CRAN - CNRS UMR 7039, Université de Lorraine, IUT de Longwy, France
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v9i1.7843

Abstract


This paper investigates the problem of the full order H∞ unknown input filter designs in time and frequency domain. The considered systems are linear singular ones with delayed states, delayed input, unknown input and bounded disturbance. Firstly, an Unknown Input Observer (UIO) and a H∞ Unknown Input Filter (H∞ UIF) for such systems are proposed respectively in the time domain. This approach is based on Lyapunov-Krasovskii stability theory, where the gain implemented in the design is an optimal solution of linear matrix inequalities (LMIs). Secondly, a frequency-domain approach is derived from time-domain results by using the factorization approach. The proposed methods show their effectiveness on an illustrative example.
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Keywords


Delayed Descriptor Systems; Frequency Domain; H∞ Filter; LMIs; MFD; Time Domain s; Unknown Inputs

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References


G. Verghese, B. Levy, T. Kailath, A generalized state-space for singular systems, IEEE Transactions on Automatic Control, pp. 811-831, 1981.
http://dx.doi.org/10.1109/tac.1981.1102763

I.S. Niculescu, Delay effect on stability, A robust control approach (Springer Verlag, 2001).

Y. Ariba, Sur la stabilité des systèmes à retards variant dans le temps : Théorie et application au contrôle de congestion d'un routeur, Université de Toulouse 3 Paul Sabatier, France, 2009.

E. K. Boukas, N. F. Al-Muthairi, Delay-dependent stabilization of singular linear systems with delays, International Journal of Innovative Computing, Information and Control, pp.283-291, 2006.

M. Ezzine, M. Darouach, H. Souley Ali, H. Messaoud, Time and Frequency domain design of Functional Filters, American Control Conference, pp. 599-604, Baltimore, MD, USA, 2010.
http://dx.doi.org/10.1109/acc.2010.5531072

M. Ezzine, M. Darouach, H. Souley Ali, H. Messaoud, Synthèse temporelle et fréquentielle de filtres H∞ d'ordre plein pour les systèmes singuliers, Confèrence Internationale Francophone d'Automatique, 2010.

D. Koenig, B. Marx, Design of Observers for descriptor systems with delayed state and unknown inputs, American Control Conference, pp.4806-4810, 2004.

M. Ezzine, M. Darouach, H. Souley Ali, H. Messaoud, Full order H∞ filtering for Linear systems in the frequency domain : The time and frequency domain cases, International Journal of Control, Automation, and Systems, pp. 558-565, 2011.
http://dx.doi.org/10.1007/s12555-011-0316-y

M. Ezzine, M. Darouach, H. Souley Ali, H. Messaoud, A controller design based on a functional H∞ filter for descriptor systems: The time and frequency domain cases, Automatica, pp. 542-549, 2012.
http://dx.doi.org/10.1016/j.automatica.2011.08.060

B.D.O. Anderson, V. Kucera, Matrix fraction construction of linear compensators, IEEE Transaction on Automatic Control, pp, 1112-1114, 1985.
http://dx.doi.org/10.1109/tac.1985.1103845

A.G.J. MacFarlane, Return-difference matrix properties for optimal stationary Kalman-Bucy filter, Proceedings of the Institution of Electrical Engineers, pp. 373-376, 1971.
http://dx.doi.org/10.1049/piee.1971.0066

N. Krasovskii, Stability of Motion (Stanford University Press, 1963).

M. Darouach, M. Boutayeb, Design of observers for descriptor systems, 40th IEEE Transactions on Automatic Control, no. 7, 1323-1327, 1995.
http://dx.doi.org/10.1109/9.400467

M. Ezzine, M. Darouach, H. Souley Ali, H. Messaoud, Unknown Inputs Functional Observers Designs For Descriptor Systems with Constant Time Delay, 18th IFAC, Milano-Italy, 2011.
http://dx.doi.org/10.1080/00207179.2013.797607

M. Vidyasagar, Control systems Synthesis: A factorization approach (M.I.T, Press, Cambridge, 1985).

P. Hippe, J. Deutscher, Design of observer based compensators: from the time to the frequency domain, Springer-Verlag, 2009.
http://dx.doi.org/10.1007/978-1-84882-537-6

M. Darouach, Linear Functional Observers for Systems with Delays in State Variables: The Discrete-Time Case, IEEE Transactions on Automatic Control, Vol. 50 No. 2, pp. 228-233, 2005.
http://dx.doi.org/10.1109/tac.2004.841932

A. Fattouh, O. Sename, J-M. Dion, Robust observer design for time-delay systems: a Riccati equation approach, Kybernetika, Vol. 35, No. 6, pp. 753-764, 1999.
http://dx.doi.org/10.1142/9789814447317_0072

J. Hale, S. Lunel, Introduction to functional differential equations (Applied Mathematical Sciences 99, Springer-Verlag, 1991).
http://dx.doi.org/10.1007/978-1-4612-4342-7_1

D. Koenig, D. Jacquet, S. Mammar, Delay-dependent H∞ observer of linear delay descriptor systems, American Control Conference, pp.3813-3817, 2006.
http://dx.doi.org/10.1109/acc.2006.1657312

I. Masubuchi, Y. Kamitane, A. Ohara, N. Suda, H∞ Control for descriptor systems: A matrix inequalities approach, Automatica, vol. 33, no. 4, pp. 669-673, 1997.
http://dx.doi.org/10.1016/s0005-1098(96)00193-8


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