Abstract
Properties of linear dynamical systems are studied in the case of Hankel singular values of high multiplicity for monosingular and bisingular systems. Singular values of the Hankel operator take only one or two values for such systems. Properties of transfer functions are analysed. Algorithms of transfer function analysis and design are developed. Relations between frequency characteristics and Hankel singular values are established.
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References
Peller, V., Hankel Operators and Their Applications, New York: Springer, 2003
Mironovskii, L.A., Hankel Operator and Hankel Functions of Linear Systems, Avtom. Telemekh., 1992, no. 9, pp. 73–86.
Francis, B.A. and Doyle, J.C., Linear Control Theory with on Hinf Optimality Criterion. A Survey, SIAM J. Control Optim., 1987, vol. 23, no. 4, pp. 815–844.
Francis, B.A., A Course in Hinf Control Theory. Lecture Notes in Control and Iformation Sci., New York: Springer, 1987, vol. 88.
Glover, K., All Optimal Hankel-Norm Approximations of Linear Multivariables Systems, Int. J. Control, 1984, vol. 39, no. 6, pp. 1115–1193.
Wilson, D.A., Convolution and Hankel Operator Norm for Linear Systems, IEEE Trans. Automat. Control, 1989, AC-34, no. 1, pp. 94–97.
Mironovskii, L.A., Funktsional’noe diagnostirovanie dinamicheskikh sistem (Functional Diagnostics for Dynamic Systems), Moscow: Mosk. Gos. Univ., 1998.
Balonin, N.A. and Mironovskii, L.A., Flip Method of Determining the Singular Functions of the Hankel Operator and the Convolution Operator, Avtom. Telemekh., 1999, no. 11, pp. 3–8.
Ober, R.J., Balanced Parameterization of Classes of Linear Systems, SIAM J. Control Optim., 1991, vol. 29, no. 6, pp. 1251–1287.
Balberin, V.V. and Mironovskii, L.A., Balanced Models for Scalar Systems, Elektronnoe Modelirovanie, 1988, no. 5, pp. 6–10.
Mironovskii, L.A. and Shintyakov, D.V., Frequency Characteristics of All-Pass and Bisingular Systems, Informatsionno-upravlyayushchie Sistemy, 2007, no. 5, pp. 36–41.
Mironovskii, L.A. and Shintyakov, D.V., All-Pass and Bisingular Systems, Proc. 8-th Sci. Session of GUAP, St. Petersburg: GUAP, 2005, vol. 2, pp. 513–515.
Anderson, B.D.O., Jury, E.I., and Mansour, M., Schwarz Matrix Properties for Continuous and Discrete Time Systems, Int. J. Control, 1976, vol. 23, pp. 1–16.
Mironovskii, L.A., Analogovye i gibridnye modeli dinamicheskikh sistem. Skalyarnye sistemy (Analog and Hybrid Models of Dynamic Systems. Scalar Systems), St. Petersburg: GUAP, 1985.
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Original Russian Text © L.A. Mironovskii, 2009, published in Avtomatika i Telemekhanika, 2009, No. 1, pp. 51–73.
This work was supported by the Russian Foundation for Basic Research, project nos. 08-08-00228.
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Mironovskii, L.A. Linear systems with multiple singular values. Autom Remote Control 70, 43–63 (2009). https://doi.org/10.1134/S0005117909010044
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DOI: https://doi.org/10.1134/S0005117909010044