WSEAS Transactions on Systems


Print ISSN: 1109-2777
E-ISSN: 2224-2678

Volume 16, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 16, 2017



A Controller Design Based on a Functional H1 Filter for Delayed Singular Systems : The Time and Frequency Domain Cases

AUTHORS: M. Khadhraoui, M. Ezzine, H. Messaoud, M. Darouach

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ABSTRACT: This paper deals with the time and frequency domain of a controller design based on a function reduced order filter for linear multi-variable delayed singular systems where measurements are affected by bounded disturbances. The control gain is designed using H1 techniques. The time procedure design is based on the unbiasedness of the estimation error using Sylvester equation and on Lyapunov-Krasovskii stability theory. Then a new method to avoid the time derivative of the disturbance in filtering error is proposed and the problem is solved by means of Linear Matrix Inequalities (LMIs). Both cases where the H1 technique is dependent or independent from the delay are dervied separetely. The frequency domain approach is derived from the time domain one by applying the factorization approach. A numerical example is given to illustrate the proposed approach.

KEYWORDS: Controller, singular systems, H1 functional filter, delay, disturbance

REFERENCES:

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

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

[3] S. Boyd and L. Vandenberghe, 'Convex Optimization', Cambridge University Press, First edition, 2004.

[4] M. Darouach, Linear Functional Filters for Systems With Delays in State Variables : The Discrete-Time Case.(2005). IEEE Transactions on Automatic Control. Vol. 50 No. 2, pp. 228- 233.

[5] M. Darouach, and M. Boutayeb, (1995). Design of filters for descriptor systems, 40thIEEE Transactions on Automatic Control, no. 7, 1323- 1327.

[6] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2010a).A controller design based on function observer for singular linear systems : Time and frequency domains approaches, 18th Mediterranean Conference, pp. 413-418, Marrakech, Morocco.

[7] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2010b). Time and Frequency domain design of Functional Filters, American Control Conference, pp. 599-604, Baltimore, MD, USA.

[8] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2010c). Synthése temporelle et fréquentielle de filtres H∞ d’ordre plein pour les systèmes singuliers

[Design of full order H∞ filters for singular systems in the time and the frequency domain] ,Conférence Internationale Francophone d’Automatique, Nancy, France.

[9] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2011a). Unknown Inputs Functional Filters Designs for Descriptor Systems with Constant Time Delay,18th IFAC, MilanoItaly.

[10] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2011b). 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.

[11] M. Ezzine, M. Darouach, H. Souley Ali and H. Messaoud, (2012). A controller design based on a functional H∞ filter for descriptor systems : The time and frequency domain cases,Automatica, pp. 542-549.

[12] A. Fattouh, O. Sename and J-M. Dion,D. Koenig, D. Jacquet and S. Mammar, Robust filter design for time-delay systems: a Riccati equation approach,Kybernetika, Vol. 35, No. 6, pp. 753-764.

[13] J. Hale, and S. Lunel, (1991). Introduction to functional differential equations,Applied Mathematical Sciences 99, Springer-Verlag.

[14] M. Khadhraoui, M. Ezzine, H. Messaoud, and M. Darouach, (2014a). Design of full order unknown input observers for delayed singular systems with tate variable time delay, International Symposium on Communications, Control and Signal Processing (ISCCSP2014), pp. 624-627, Athens, Grec.

[15] M. Khadhraoui, M. Ezzine, H. Messaoud, and M. Darouach, (2014b). Functional Observers design with unknown inputs for delayed singular systems : The discrete time case, Mediterranean Conference of Control and Automation (MED2014c), pp. 127-132, Palermo, Italy.

[16] M. Khadhraoui, M. Ezzine, H. Messaoud, and M. Darouach, (2014c). Design of Full Order H∞ Filter for Delayed Singular Systems with Unknown Input and Bounded Disturbance, International Conference on Control, Decision and Information Technologies (CODIT2014), pp. 429-434, Metz-France.

[17] M. Khadhraoui, M. Ezzine, H. Messaoud, and M. Darouach, (2014d). Design of Full Order ObWSEAS servers with Unknown Inputs for Delayed Singular Systems with Constant Time Delay, International Conference on Control, Decision and Information Technologies (CODIT2014), pp. 423- 428, Metz-France.

[18] D. Koenig, D. Jacquet and S. Mammar, (2006). Delay-dependent H∞ filter of linear delay descriptor systems,Proc. American Control Conference, pp.3813-3817, Minneapolis, MN, USA.

[19] D. Koenig and B. Marx, (2004). Design of Observers for descriptor systems with delayed state and unknown inputs,Proc. American Control Conference, pp.4806-4810, Boston, MA, USA.

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

[21] I. Masubuchi, Y. Kamitane, A. Ohara and N. Suda, (1997). H∞ Control for descriptor systems: A matrix inequalities approach,Automatica, vol. 33, no. 4, pp. 669-673.

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

[23] Verghese, G., Levy, B. and Kailath, T. (1981). A generalized state-space for singular systems,IEEE Transactions on Automatic Control, pp. 811-831.

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

[25] S. Xu, B. J. Lam and C. Yang, (2003). Robust H∞ control for uncertain singular systems with state delay,International Journal of Robust and Nonlinear Control, vol. 13, pp. 1213-1223.

WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 16, 2017, Art. #17, pp. 131-148


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