Abstract
This work is a continuation of [2] and [1] in which the authors studied the preservation of the observability and observer under sampling. In this paper, by relaxing some hypotheses, we study the observability and stabilization problems for a sampled bilinear system. We give a characterization of the observability for such systems. Moreover, under some sufficient conditions, we show that the sampled of the bilinear system can be globally asymptotically stabilizable using a state observer.
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References
S. Ammar, Observability and observateur under sampling. Int. J. Control 79 (2006), No. 9, 1039–1045.
S. Ammar and J.-C. Vivalda, On the preservation of observability under sampling. Syst. Control Lett. 52 (2004), 7–15.
M. Bensoubaya, A. Ferfera, and A. Iggidr, New results on the stability of discrete-time systems and applications to control problems. J. Math. Anal. Appl. 219 (1998), 392–414.
S. Celikovský, On the global linearization of bilinear systems. Syst. Control Lett. 15 (1990), 433–439.
R. Chabour, G. Sallet, and J. C. Vivalda, Stabilization of nonlinear two dimensional systems: A bilinear approach. Math. Cont. Sign. Syst. (1996), 224–246.
R. Chabour and J. C. Vivalda, Stabilisation des systemes bilineaires dans le plan par une commande non reguliere. Proc. Eur. Control Conf. ECC’91, Grenoble, France (1991), pp. 485–487.
B. D’Andrea-Novel and M. Cohen de Lara. Commande lineaire des systemes dynamiques. Presses de l’Ecole des Mines de Paris, September (2000).
J.-P. Gauthier and I. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994), No. 4, 975–994.
J. P. Gauthier and I. Kupka, A separation principle for bilinear systems with dissipative drift. IEEE Trans. Automat. Control 37 (1992), No. 12, 1970–1974.
R. Hermann and A.-J. Krener, Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977), 728–740.
H. Jerbi, Global feedback stabilization of new class of bilinear systems. Syst. Control Lett. 42 (2001), 313–320.
M. A. Hammami, Global convergence of a control system by means of an observer. J. Optim. Theory Appl. 108 (2001), No. 2, 377–388.
E. D. Sontag, On the preservation of certain controllability properties under sampling. In: Outils et modules mathématiques pour l’automatique, l’analyse de systémes et le traitement du signal (I. D. Landau, Ed.). Edition du CNRS, Paris (1983), No. 3, pp. 623–637.
_____, A concept of local observability. Syst. Control Lett. 5 (1984), 41–47.
V. Sundarapandian, Global asymptotic stability of nonlinear cascade systems. Appl. Math. Lett. 15 (2002), 275–277.
_____, General observers for discrete-time nonlinear systems. Math. Comput. Modelling 39 (2004), 87–95.
_____, Local and global asymptotic stability of nonlinear cascade interconnected systems. Math. Comput. Modelling 40 (2004), 227–232.
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Ammar, S., Hammami, M.A., Jerbi, H. et al. Separation principle for a sampled bilinear system. J Dyn Control Syst 16, 471–484 (2010). https://doi.org/10.1007/s10883-010-9102-z
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DOI: https://doi.org/10.1007/s10883-010-9102-z