Non-Frobenius Spectrum-Transformation Method

Abstract

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.

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.