Theoretical observers for infinite dimensional skew-symmetric systems

[1] Curtain, R. F., Pritchard, A. J., Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, vol. 8, Springer-Verlag, Berlin, 1978.10.1007/BFb0006761Search in Google Scholar

[2] Curtain, R. F., Weiss, G., Well posedness of triples of operators (in the sense of linear systems theory). Control and estimation of distributed parameter systems (Vorau, 1988), Internat. Ser. Numer. Math., vol.91, Birkhauser, Basel, 1989, pp. 41–59.Search in Google Scholar

[3] Curtain, R. F., Zwart, H., An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics, voL. 21, Springer-Verlag, New York, 1995.10.1007/978-1-4612-4224-6Search in Google Scholar

[4] Davies, E. B., One-parameter semigroups, Academic Press, London, 1980.Search in Google Scholar

[5] Deguenon, J. Observateurs des Systemes Anti-Adjoints de Dimension Infinie et Application, These unique de doctorat, Universite de Metz, Metz, France, 2003.Search in Google Scholar

[6] Deguenon, A. J., Sallet, G., Xu, C. Z. A Luenberger observer for infinite dimensional skew-symmetric systems with application to an elastic beam, Proc. 2nd Int. Symp on Comm. Control and Signal, Marrakech, 2006.Search in Google Scholar

[7] Jacob, B., Partington J., Admissibility of Control and Observation Operators for Semigroups: A Survey. In: Ball J.A., Helton J.W., Klaus M., Rodman L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149, Birkhuser, Basel, 2004.Search in Google Scholar

[8] El Jai, A., Pritchard, A.J. Capteurs et actionneurs dans l’analyse des systemes distribues, Masson, New York, 1986, 203 p.Search in Google Scholar

[9] Fuhrmann, P. A. Linear systems and operators in Hilbert space, McGraw-Hill International Book Co., New York, 1981.Search in Google Scholar

[10] Jurjevic, V., Quinn, J.P. Controlability and stability, Journal of Differential Equations, vol. 28, 1978, pp. 381–389.10.1016/0022-0396(78)90135-3Search in Google Scholar

[11] Pazy, A. Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983, 296 p.10.1007/978-1-4612-5561-1Search in Google Scholar

[12] Pritchard, A. J., D. Salamon, D., The linear quadratic control problem for infinite-dimensional systems with unbounded input and output operators, SIAM J. Control Optim., vol. 25(1), 1987, pp. 121–144.10.1137/0325009Search in Google Scholar

[13] Russell, D. L., Weiss, G., A general necessary condition for exact observability, SIAM J. Contr. Optim., vol. 32, 1994, pp. 1–2310.1137/S036301299119795XSearch in Google Scholar

[14] Salamon, D., Control and observation of neutral systems, Research Notes in Mathematics, Pitman (Advanced Publishing Program), vol.91, Boston, MA, 1984.Search in Google Scholar

[15] Salamon, D., Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc., vol. 300(2), 1987, pp. 383–431.10.2307/2000351Search in Google Scholar

[16] Salamon, D., Realization theory in Hilbert space, Math. Systems Theory, vol. 21, 1989, pp. 147–164.10.1007/BF02088011Search in Google Scholar

[17] Slemrod, M. A note on complete controllability and stabilizability for linear control systems in Hilbert spaces, SIAM J. Contr. Optim., vol. 12, 1974, pp. 500–508.10.1137/0312038Search in Google Scholar

[18] Weiss, G., The representation of regular linear systems on Hilbert spaces, Control and estimation of distributed parameter systems (Vorau, 1988), Internat. Ser. Numer. Math., vol.91, Birkhauser, Basel, 1989, pp. 367–378.Search in Google Scholar

[19] Weiss, G. Regular linear systems with feedback, Mathematics of Control, Signals, and Systems, vol. 7, 1994, pp. 23–57.10.1007/BF01211484Search in Google Scholar

[20] Weiss, G. Two conjectures on the admissibility of control operators, International Series of Numerical Mathematics, vol. 100, 1991, pp. 367–378.10.1007/978-3-0348-6418-3_26Search in Google Scholar

[21] Weiss, G., Curtain, F. Dynamic stabilization of regular linear systems, IEEE Transaction Automatic Control, 42, 1997, pp. 4–21.10.1109/9.553684Search in Google Scholar

[22] Weiss, G.,Curtain, R.F. Exponential stabilization of vibrating systems by collocated feedback, Proc. 7th IEEE Mediterranean Symposium on Control and Automation, June 28 - 30, 1999, Haifa, Israel, pp. 1705 – 1722.Search in Google Scholar

[23] Weiss, G., Curtain, R.F., Exponential stabilization of a Rayleigh beam using collocated control, IEEE Trans. Automatic Control, 53, issue 3, 2008, pp. 643 – 654.10.1109/TAC.2008.919849Search in Google Scholar

[24] Xu, C.Z. Contrôle des systemes hybrides, Polycopie du Cours de DEA, Institut de Mathématiques et de Sciences Physiques, Bénin, 1999.Search in Google Scholar