References
J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory: A Behavioral Approach (Springer-Verlag, Berlin, 1997).
R. E. Kalman, P. Falb, and M. Arbib, Topics in Mathematical System Theory (McGraw-Hill, New York, 1969; Mir, Moscow, 1971).
V. A. Rusanov, Dokl. Math. 82, 676–678 (2010).
V. A. Rusanov, A. V. Lakeev, and Yu. È. Linke, Dokl. Math. 83, 430–432 (2011).
V. A. Rusanov, L. V. Antonova, and A. V. Daneev, Adv. Differ. Equations Control Proc. 10(2), 69–88 (2012).
A. N. Kolmogorov, Selected Works, Vol. 1: Mathematics and Mechanics (Nauka, Moscow, 2005), pp. 296–300 [in Russian].
V. A. Rusanov and D. Yu. Sharpinskii, Prikl. Math. Mekh. 74(1), 119–132 (2010).
S. K. Korovin, A. P. Krishchenko, and V. N. Chetverikov, Dokl. Math. 82, 838–842 (2010).
K. Yosida, Functional Analysis (Academic, New York, 1965; Mir, Moscow, 1967).
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces (Academic, New York, 1966; Mir, Moscow, 1970).
I. V. Sergienko and V. S. Deineka, Kibern. Sist. Anal., No. 4, 28–50 (2011).
P. Eykhoff, System Identification (Wiley, New York, 1974; Mir, Moscow, 1975).
R. Engelking, General Topology (Heldermann-Verlag, Berlin, 1989; Mir, Moscow, 1986).
H. von Weizsäcker, Math. Scand. 38(2), 321–324 (1976).
C. Bessaga and T. Dobrowolski, Proc. Am. Math. Soc. 125(1), 259–268 (1997).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Rusanov, A.V. Lakeev, Yu.è. Linke, 2013, published in Doklady Akademii Nauk, 2013, Vol. 451, No. 1, pp. 24–27.
Rights and permissions
About this article
Cite this article
Rusanov, V.A., Lakeev, A.V. & Linke, Y.È. A differential realization of an input-output autonomous nonlinear system of minimal dynamic order in a Hilbert space. Dokl. Math. 88, 499–502 (2013). https://doi.org/10.1134/S1064562413040042
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562413040042