Controllability of infinite-dimensional systems with delays in control
Abstract
This paper considers the various types of controllability of linear infinite-dimensional dynamical systems defined in a Banach space, with multiple time-varying delays in control. Necessary and sufficient conditions for approximate controllability, approximate relative controllability and approximate absolute controllability of these systems are obtained. Special cases of systems defined in a Hilbert space are also considered.
References
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2. M.C. Delfour, S.K. Mitter, Controllability and observability for infinite-dimensional systems, SIAM J. Control Optim. 10 (1972), 329-333.
3. H.O. Fattorini, Some remarks on complete montrollability, SIAM J. Control Optim. 4 (1966), 686-694.
4. H.O. Fattorini, Boundary control of temperature distributions in a parallelepipedan, SIAM J. Control Optim. 13 (1975), 1-13.
5. H.O. Fattorini, D.L. Russell, Exact controllability theorems for linear parabolitic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971), 272-292.
6. J. Klamka, Controllability of linear systems with time-variable delays in control, Informat. J. Control 24 (1976), 869-878.
7. J. Klamka, Absolute controllability of linear systems with time-variable delays in control, Systems Sci. 4 (1978), 43-52.
8. J. Klamka, Relative controllability of infinite-dimensional systems with delays in control, Systems Sci. 4 (1978), 43-52.
9. A.W. Olbrot, On the controllability of linear systems with time delays in control, IEEE Trans. Automat. Control 17 (1972), 664-666.
10. D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies in Appl. Math. 52 (1973), 189-211.
11. Y. Sakawa, Controllability for partial differential equations of parabolic type, SIAM J. Control Optim. 12 (1974), 389-400.
12. T.I. Seidman, Observation and prediction for the heat equation. IV: Patch observability and controllability, SIAM J. Control Optim. 15 (1977), 412-427.
13. R. Triggiani, Controllability and observability in Banach space with bounded operators, SIAM J. Control Optim. 13 (1975), 462-491.
14. R. Triggiani, Extensions of rank conditions for controllability and observability to Banach space and unbounded operators, SIAM J. Control Optim. 14 (1976), 313-338.
15. R. Triggiani, On the lack of exact controllability for mild solutions in Banach space, J. Math. Anal. Appl. 50 (1975), 438-446.
KlamkaJ. (1985). Controllability of infinite-dimensional systems with delays in control. Annales Mathematicae Silesianae, 1, 51-65. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14336
Jerzy Klamka
Instytut Automatyki, Politechnika Śląska Poland
Instytut Automatyki, Politechnika Śląska Poland
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