Geodesic
Boundary control and canonical realizations of a~two-velosity dynamical system
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 18-44

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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. 
@article{ZNSL_1995_222_a1,
     author = {M. I. Belishev and S. A. Ivanov},
     title = {Boundary control and canonical realizations of a~two-velosity dynamical system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {18--44},
     publisher = {mathdoc},
     volume = {222},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a1/}
}
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M. I. Belishev; S. A. Ivanov. Boundary control and canonical realizations of a~two-velosity dynamical system. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 18-44. http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a1/