Non-Frobenius Spectrum-Transformation Method


A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix. The method can be used for simulation of systems with different spectrums for choosing an alternative that satisfies to the distinct demands.

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A. Iskhakov, V. Pospelov and S. Skovpen, "Non-Frobenius Spectrum-Transformation Method," Applied Mathematics, Vol. 3 No. 10A, 2012, pp. 1471-1479. doi: 10.4236/am.2012.330206.

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[1] R. Gabasov and F. M. Kirillova, “Mathematical Theory of Optimal Control. Results of Since and Engineering,” Mathematical Analysis, Vol. 16, 1979, pp. 55-97.
[2] G. G. Islamov, “On the Control of a Dynamical System Spectrum,” Differential Equations, Vol. 23, No. 8, 1987, pp. 1299-1302.
[3] N. T. Kuzovkov, “Modal Control and Observe Devices,” Mashinostroenie, Moscow, 1976.
[4] A. A. Krasovsky, “Control Theory Reference Book,” Nauka, Moscow, 1987.
[5] G. A. Leonov and M. M. Shumafov, “The Methods for Linear Controlled System Stabilization,” St.-Petersburg University Publisher, St.-Petersburg, 2005.
[6] V. V. Voevodin and Y. A. Kuznetsov, “Matrices and Calculations,” Nauka, Moscow, 1984.
[7] R. Isermann, “Digital Control Systems,” Springer-Verlag, New York, 1996.

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