Abstract
An overview is presented of results which show the central role of the cascade structure in linear system theory. The first group of results is related to the recursive realization problem while the second group of results is related to passive network synthesis.
Support was provided by N.S.F. through Grant ECS - 05293.
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References
A. C. Antoulas [1986], On recursiveness and related topics in linear systems, IEEE-AC 31: 1121–1135.
A. C. Antoulas and R. H. Bishop [1987], Continued fraction decomposition of linear systems in the state space, Systems and Control Letters, 9: 43–53.
N. Balabanian and T. Bickart [1981], Linear network theory, Matrix Publishers.
Ph. Delsarte, Y. Genin, and Y. Kamp [1979], The Nevanlinna-Pick problem for matrix-valued functions, SIAM J. Appl. Math., 36: 47–61.
Ph. Delsarte, Y. Genin, and Y. Kamp [1981], On the role of the Nevanlinna-Pick problem in circuit and system theory, Int. J. Circuit Theory Appl., 9: 177–187.
P. Dewilde and H. Dym [1989], Inverse scattering and networks, short course given during the MTNS-89 Symposium, Amsterdam, June 19–23.
P. A. Fuhrmann [1983], A matrix Euclidean algorithm and matrix continued fraction expansion, Systems & Control Letters, 3: 263–271.
F. R. Gantmacher [1960], Matrix theory, 2 volumes, Chelsea.
R. E. Kalman, P. L. Falb, and M. A. Arbib [1969], Topics in mathematical system theory, McGraw-Hill.
R. E. Kalman [1979], On partial realizations, transfer functions, and canonical forms, Acta Polytechnica Scandinavica, Ma31: 9–32.
T. Kailath [1980], Linear systems, Prentice Hall.
P. P. Vaidyanathan and S. K. Mitra [1987], A unified structural interpretation of some well-known stability-test procedures for linear systems, Proc. IEEE, 75: 478–497.
J. C. Willems and A. C. Antoulas [1989], Recursive time series modeling, Technical Report, Department of Mathematics, E. T. H. Zurich.
J. C. Willems [1986–1987], From time series to linear system, Automatica; Part I: Finite dimensional linear time invariant systems, 22: 561–580; Part II: Exact modeling, 22: 675–694; Part III: Approximate modeling, 23: 87–115.
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© 1989 Springer-Verlag
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Antoulas, A.C. (1989). The cascade structure in system theory. In: Nijmeijer, H., Schumacher, J.M. (eds) Three Decades of Mathematical System Theory. Lecture Notes in Control and Information Sciences, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008456
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DOI: https://doi.org/10.1007/BFb0008456
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