Inverse Matrix in the Theory of Dynamic Systems

Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1107227

References:

[1] D. K. Fadejev, V. N. Fadejeva, “Numerické metody lineární algebry,” SNTL, Praha, 1964.
[2] J. Štecha, V. Havlena. “Teorie dynamických systémú,” ČVUT, Praha, 2005.
[3] P. Dorato, “On the Inverse of Linear Dynamical Systems,” IEEE Transactions on systems science and cybernetics, vol. ssc-5, no.1, 1969, pp. 43–48.
[4] L. M. Silverman, “Inversion of Multivariable Linear Systems,” IEEE Transactions on automatic control, vol. ac-14, no.3, 1969, pp. 270–276.
[5] P. Zlatoš, “Lineárna algebra a geometria,” Martinus, Bratislava, 2011.
[6] P. Sankowski, “Dynamic Transitive Closure via Dynamic Matrix Inverse,” 45th Annual IEEE Symposium on Foundations of Computer Science, 2004.
[7] Wang Menfu, F. T. K. Au, “Precise integration method without inverse matrix calculation for structural dynamic equation,” Earthquake engineering and engineering vibration, vol. 6, no.1, 2007, pp. 57–64.
[8] U. Helmke, P. A. Fuhlmann, “Controllability of matrix eigenvalue algorithms: the inverse power method,” Systems & Control Letters 41, 2000, pp. 57–66.
[9] S. Pavlikova, “Extending the Class of Matrices Invertable using Graphs,” 6th Convergence on Mathematics and Physics at Technical Universitie 2009, pp. 203-210.
[10] S. Pavlikova, J. Krč-Jediny, “On the Inverse and the Dual Index of a Tree,” Linear and Multilinear Alhebra,, vol. 28,1990, pp.93- 109.
[11] “MATLAB® Math. For Use with MATLAB®.” Massachusets: The MathWorks, Inc., 2006.
[12] A. Gilat, “Solution manual for MATLAB: An Introduction with Applications, SI Version,” John Wiley & Sons Ltd., 2011.