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Unbounded perturbations of the generator domain
1. | Department of Mathematics, Faculty of Sciences, Ibn Zohr University, B.P. 8106, Agadir, Morocco |
2. | Department of Information Engineering and Applied Mathematics, University of Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italy |
3. | Dept. of Information Eng., Electrical Eng. and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, I 84084 Fisciano (SA), Italy |
References:
[1] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, Representation and Control of Infinite-Dimensional Systems, Birkhäuser, Boston, Basel, Berlin, 2007. |
[2] |
A. Chen and K. Morris, Well-posedness of boundary control systems, SIAM J. Control Optim., 42 (2003), 1244-1265.
doi: 10.1137/S0363012902384916. |
[3] |
R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, TAM 21, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[4] |
K. J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000. |
[5] |
K. J. Engel, M. Kramar, B. Klöss, R. Nagel and E. Sikolya, Maximal controllability for boundary control problems, Appl. Math. Optim., 62 (2010), 205-227.
doi: 10.1007/s00245-010-9101-1. |
[6] |
H. O. Fattorini, Boundary control systems, SIAM J. Control, 6 (1968), 349-385.
doi: 10.1137/0306025. |
[7] |
G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. |
[8] |
S. Hadd, A. Idrissi and A. Rhandi, The regular linear systems associated with the shift semigroups and application to control linear systems with delay, Math. Control Signals Systems, 18 (2006), 272-291.
doi: 10.1007/s00498-006-0002-4. |
[9] |
M. Kumpf and G. Nickel, Dynamic boundary conditions and boundary control for the one-dimensional heat equation, J. Dynam. Control Systems, 10 (2004), 213-225.
doi: 10.1023/B:JODS.0000024122.71407.83. |
[10] |
D. Salamon, Infinite-dimensional linear system with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc., 300 (1987), 383-431.
doi: 10.2307/2000351. |
[11] |
O. J. Staffans, Well-posed Linear Systems, Encyclopedia of Mathematics and its Applications, 103, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511543197. |
[12] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Birkhäuser, Basel, Boston, Berlin, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[13] |
G. Weiss, Admissible observation operators for linear semigroups, Israel J. Math., 65 (1989), 17-43.
doi: 10.1007/BF02788172. |
[14] |
G. Weiss, Admissibility of unbounded control operators, SIAM J. Control Optim., 27 (1989), 527-545.
doi: 10.1137/0327028. |
[15] |
G. Weiss, Transfer functions of regular linear systems. I. Characterization of regularity, Trans. Amer. Math. Soc., 342 (1994), 827-854.
doi: 10.2307/2154655. |
[16] |
G. Weiss, Regular linear systems with feedback, Math. Control Signals Systems, 7 (1994), 23-57.
doi: 10.1007/BF01211484. |
show all references
References:
[1] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, Representation and Control of Infinite-Dimensional Systems, Birkhäuser, Boston, Basel, Berlin, 2007. |
[2] |
A. Chen and K. Morris, Well-posedness of boundary control systems, SIAM J. Control Optim., 42 (2003), 1244-1265.
doi: 10.1137/S0363012902384916. |
[3] |
R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, TAM 21, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4224-6. |
[4] |
K. J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000. |
[5] |
K. J. Engel, M. Kramar, B. Klöss, R. Nagel and E. Sikolya, Maximal controllability for boundary control problems, Appl. Math. Optim., 62 (2010), 205-227.
doi: 10.1007/s00245-010-9101-1. |
[6] |
H. O. Fattorini, Boundary control systems, SIAM J. Control, 6 (1968), 349-385.
doi: 10.1137/0306025. |
[7] |
G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. |
[8] |
S. Hadd, A. Idrissi and A. Rhandi, The regular linear systems associated with the shift semigroups and application to control linear systems with delay, Math. Control Signals Systems, 18 (2006), 272-291.
doi: 10.1007/s00498-006-0002-4. |
[9] |
M. Kumpf and G. Nickel, Dynamic boundary conditions and boundary control for the one-dimensional heat equation, J. Dynam. Control Systems, 10 (2004), 213-225.
doi: 10.1023/B:JODS.0000024122.71407.83. |
[10] |
D. Salamon, Infinite-dimensional linear system with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc., 300 (1987), 383-431.
doi: 10.2307/2000351. |
[11] |
O. J. Staffans, Well-posed Linear Systems, Encyclopedia of Mathematics and its Applications, 103, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511543197. |
[12] |
M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups, Birkhäuser, Basel, Boston, Berlin, 2009.
doi: 10.1007/978-3-7643-8994-9. |
[13] |
G. Weiss, Admissible observation operators for linear semigroups, Israel J. Math., 65 (1989), 17-43.
doi: 10.1007/BF02788172. |
[14] |
G. Weiss, Admissibility of unbounded control operators, SIAM J. Control Optim., 27 (1989), 527-545.
doi: 10.1137/0327028. |
[15] |
G. Weiss, Transfer functions of regular linear systems. I. Characterization of regularity, Trans. Amer. Math. Soc., 342 (1994), 827-854.
doi: 10.2307/2154655. |
[16] |
G. Weiss, Regular linear systems with feedback, Math. Control Signals Systems, 7 (1994), 23-57.
doi: 10.1007/BF01211484. |
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