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.
Main publications:
Passive linear stationary dynamical scattering systems with continuous time // Integral Equations and Operator Theory, 1996, vol. 24, no 1, p. 1–45.
