| Abstract: | The paper is devoted to the problems of controllability and realization for dynamical systems with various types of interacting
waves that propagate with different velocities. One-velocity and a two-velocity dynamical systems are significantly different
from the physical point of view. One can reconstruct a one-velocity system by its transfer function. For a two-velocity system
a unique reconstruction is impossible. A procedure is proposed that allows us to construct by a transfer function of a two-velocity
system a one-velocity system (a model) with the same transfer function. We give a “dynamical” interpretation for the triangular
Krein factorization and for the corresponding construction of a triangular integral. For a transformation operator that connects
a two-velocity system and its one-velocity model, a representation is given in terms of projectors on the accessible sets.
Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1994, pp. 18–44. |
