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

The paper is devoted to the problems of controllability and realization of the dynamical systems with two types of interacting waves propagating with different velocities. A characteristic description of the reachable sets is found. The existence of the canonical realization (model) of two-velocity system is proved (the model is a one-velocity system having the same transfer operator-function). A procedure of construction of the model is based on the operator integral arising in M. Krein's triangular factorization. A dynamical interpretation of the integral is proposed. Bibliography: 7 titles.