Passive linear stationary dynamical scattering systems with continuous time

Integral Equations and Operator Theory

Volumn 24, Issue 1, 1996, Pages 1-45

  Arov, D Z ^a   Nudelman, M A ^a  

^a SOUTH UKRAINIAN NATIONAL PEDAGOGICAL UNIVERSITY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030448627     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01195483     Document Type: Article

References (34)

1. V.M. Adamjan and D.Z. Arov, On unitary couplings of semiunitary operators, Mat. issled., Kishinev 1(2) (1966), 3-66 (Russian).
2. D.Z. Arov, Scattering theory with dissipation of energy, Dokl. AN SSSR 216(4) (1974), 716-718 (Russian). English translation with addends: Soviet Math. Dokl. 15 (1974), 848-854.
3. D.Z. Arov, Scattering theory with dissipation of energy, Dokl. AN SSSR 216(4) (1974), 716-718 (Russian). English translation with addends: Soviet Math. Dokl. 15 (1974), 848-854.
4. D.Z. Arov, Passive linear stationary dynamical system, Sibirsk. Mat. Zhurn. 20(2) (1979), 211-228 (Russian).
5. D.Z. Arov, Stable dissipative linear stationary dynamical scattering systems, J. Operator Theory 2 (1979), 95-126 (Russian).
6. J.A. Ball and N. Cohen, De Branges-Rovnyak operator models and systems theory: a survey, Operator Theory: Advances and Applications 50 (1990), 93-136.
7. Yu.M. Berezansky, Decomposition Respectively to the Eigen Functions of the Selfadjoint Operators, Naukova Dumka, Kiev, 1965, 798 pp.
8. D.A. Bondy, An application on functional operator models to dissipative scattering theory, Trans. Amer. Math. Soc. 223 (1976), 1-43.
9. L. de Branges, Hilbert Spaces of Entire Functions, New Jersay, 1968.
10. M.S. Brodsky, Triangular and Jordan Representations of Linear Operators, Nauka, Moscow, 1969, 289 pp. (Russian).
11. M.S. Brodsky, The unitary operator nodes and their characteristic functions, Uspehi Math. Nauk. 33(4) (1978), 141-168.
12. C. Foias, On the Lax-Phillips nonconservative scattering theory, J. Funct. Anal., 19(3) (1975), 273-301.
13. J.W. Helton, The characteristic functions of operator theory and electrical network realization, Indiana Univ. Math. J. 22 (1972), 403-414.
14. J.W. Helton, Discrete time systems, operator models, and scattering theory, J. Funct. Anal. 16 (1974), 15-38.
15. J.W. Helton, Systems with infinite-dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), 145-160.
16. H. Helson, Lectures on Invariant Subspaces, New York, London, 1964.
17. D.J. Hill and P.J. Moylan, Dissipative dynamical systems: basic input-output and state properties, J. Franklin Inst. 309 (1980), 327-357.
18. E. Hille and R. Phillips, Functional Analysis and Semigroups, Providence, 1957.
19. P. Lax and R. Phillips, Scattering Theory, New York, 1967.
20. P. Lax and R. Phillips, Scattering theory for dissipative hyperbolic systems, J. Funct. Anal. 14(2) (1975), 172-235.
21. M.S. Livsiĉ, Operators, Vibrations, Waves. Open Systems, Nauka, Moscow, 1966, 298 pp.
22. M.S. Livsiĉ and A.A. Yantsevich, The Theory of the Operator Nodes in the Hilbert Spaces, Kharkov, 1977, 160 pp.
23. M.S. Livsiĉ, On a class of the linear operators in the Hilbert Space, Math. Sbornik. 19 (1946), 239-260.
24. B.S. Nagy and C. Foias, Harmonic Analysis of Operators in Hilbert Space, Mir, Moscow, 1970, 427 pp. (Russian).
25. N.K. Nikolskii and V.O. Vasyunin, A unified approach to function models and the transcription problem, in The Gohberg Anniversary Collection, Vol. 41 (H. Dym, S. Goldberg, M.A. Kaashoek and P. Lancaster, eds.), Birkhäuser-Verlag, OT 41, Basel, pp. 405-434.
26. M.A. Nudelman, Optimal passive systems and semiboundedness of quadratic functionals, Siberian Math. J. XXXIII (1) (1992), 78-86 (Russian).
27. M.A. Nudelman, The sufficient conditions of absolute stability of optimal passive scattering systems, Algebra i Analiz. 6(4) (1994) (Russian), to appear.
28. R. Ober and S. Montgomery-Smith, Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions, SIAM J. Control Opt. 28 (1990), 438-465.
29. R. Ober and W. Yuanyin, Infinite dimensional continuous time linear systems: stability and structure analysis, Technical Report 1, Center for Engineering Mathematics, The University of Texas at Dallas.
30. D. Salamon, Realization theory in Hilbert space, Math. Systems Theory 21 (1989), 147-164.
31. Yu.L. Shmuljan, Invariant subspaces of semigroups and Lax-Phillips scheme, Dep. in VINITI, No. 8009-B86, Odessa, 1986, 49 pp.
32. E.R. Tsekanovsky and Yu.L. Shmuljan, The theory of the biextensions of the operators, Uspehi Math. Nauk. 32(5) (1977), 69-124.
33. G. Weiss, Transfer functions of regular linear systems, Trans. Amer. Math. Soc., to appear.
34. J.C. Willems, Dissipative Dynamical Systems, Part I: General Theory, Part II: Linear Systems with Quadratic Supply Rates, Archive for Rational Mechanics and Analysis, Vol. 45, Springer-Verlag, 1972, pp. 321-393.