Boundary control and canonical realizations of a two-velocity dynamical system

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.