By the V. A. Yakubovich method of semibounded quadratic functionals the problem of absolute stability for the systems of ordinary differential equations in degenerate case and for the systems of differential equations with delay in singular case is investigated. By the same method the existence of optimal F–passive system with discrete time is proved. For infinite-dimensional passive scattering systems the sufficient conditions for strong and weak absolute stability are found. Joint with D. Z. Arov the theory of passive and conservative scattering systems with continuous time is developed. The global existence theorem for such systems with nonlinear feedback is proved. The conservative scattering system describing small oscillations of nonhomogeneous string is constructed which allowed to apply in the theory of Krein string the apparatus of characteristic functions of nonselfadjoint operators. The generalization of M. G. Krein and A. A. Nudelman result about completeness of the string operator is obtained.
Biography
Graduated from the Faculty of Mechanics and Mathematics of Odessa State University in 1984 (department of methods of mathematical physics). Ph.D. thesis was defended in 1993. A list of my works contains 21 title.
Main publications:
Passive linear stationary dynamical scattering systems with continuous time // Integral Equations and Operator Theory, 1996, vol. 24, no 1, p. 1–45.
D. Z. Arov, M. A. Nudelman, “Tests for the similarity of all minimal passive realizations of
a fixed transfer function (scattering or resistance matrix)”, Mat. Sb., 193:6 (2002), 3–24; Sb. Math., 193:6 (2002), 791–810
M. A. Nudelman, “The Krein string and characteristic functions of maximal dissipative operators”, Zap. Nauchn. Sem. POMI, 290 (2002), 138–167; J. Math. Sci. (N. Y.), 124:2 (2004), 4918–4934
M. A. Nudelman, “Passive scattering systems with nonlinear feedback”, Differ. Uravn., 35:11 (1999), 1492–1495; Differ. Equ., 35:11 (1999), 1512–1515
1994
4.
M. A. Nudelman, “Sufficient conditions for the absolute stability of optimal passive scattering systems”, Algebra i Analiz, 6:4 (1994), 187–203; St. Petersburg Math. J., 6:4 (1995), 865–877
M. A. Nudelman, “Optimal passive systems and semiboundedness of quadratic functionals”, Sibirsk. Mat. Zh., 33:1 (1992), 78–86; Siberian Math. J., 33:1 (1992), 62–69
M. A. Nudelman, “A singular case of a problem on the absolute stability of systems with delay (with scalar control)”, Sibirsk. Mat. Zh., 32:5 (1991), 112–125; Siberian Math. J., 32:5 (1991), 822–834
1989
7.
M. A. Nudelman, “A special case of a problem on the absolute stability of systems of ordinary differential equations”, Sibirsk. Mat. Zh., 30:1 (1989), 194–198; Siberian Math. J., 30:1 (1989), 150–153
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