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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics
Observability of a class of linear dynamic infinite systems on time scales; 347-358

Dorota Mozyrska, Zbigniew Bartosiewicz

Linear dynamic systems with output, evolving on the space Roo of infinite sequences, are studied. They are described by infinite systems of Δ-differential linear equations with row-finite matrices, for which time belongs to an arbitrary time scale. Such systems generalize discrete-time and continuous-time row-finite systems on Roo studied earlier. Necessary and sufficient conditions on observability of such systems are given. Formal polynomial series on time scales are introduced.


1. Bartosiewicz, Z. and Pawłuszewicz, E. Realizations of linear control systems on time scales. Control Cybern., 2006, 35, 769–786.

2. Bartosiewicz, Z. and Mozyrska, D. Observability of infinite-dimensional finitely presented discrete-time linear systems. Zesz. Nauk. Politech. Białostockiej. Mat.-Fiz.-Chem., 2001, 20, 5–14.

3. Bartosiewicz, Z. and Mozyrska, D. Observability of row-finite countable systems of linear differential equations. In Proceedings of 16th IFAC Congress, 4–8 July 2005, Prague (Piztek, P., ed.). Elsevier, Oxford, 2006.

4. Curtain, R. F. and Zwart, H. An Introduction to Infinite-Dimensional Linear Systems Theory. Springer-Verlag, New York, 1995.

5. Banach, S. Théorie des opérations linéaires. Warsaw, 1932.

6. Mozyrska, D. and Bartosiewicz, Z. Dualities for linear control differential systems with infinite matrices. Control Cybern., 2006, 36, 887–904.

7. Deimling, R. Ordinary Differential Equations in Banach Spaces. Lecture Notes Math., Vol. 596. Springer-Verlag, 1977.

8. Cooke, R. G. Infinite Matrices and Sequence Spaces. Macmillan, London, 1950.

9. Agarwal, R. P. and Bohner, M. Basic calculus on time scales and some of its applications. Results Math., 1999, 35, 3–22.

10. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales. Birkhauser, Boston, 2001.

11. Bohner, M. and Lutz, A. Asymptotic expansions and analytic dynamic equations.

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