Abstract
The numerically stable Larin’s algorithm is used for constructing bloc triangular or diagonal form of a matrix separating its spectrum into the “stable” and “unstable” parts. Various control problems (distinguishing the stable or unstable parts of a linear stationary control system, rational separation, algebraic Riccati equations and polynomial factoring) are solved by using this form. The corresponding software is written in language Turbo C, and the known model example is given.
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References
Aliev, F.A., Bordyug, B.A. and Larin, V.B., 1986, Methods for solving matrix algebraic Riccati equations (in Russian), Prepr., Inst. Fiz. Akad. Nauk Azerb. SSR, n. 189.
Aliev, F.A., Bordyug, B.A. and Larin, V.B., 1987, The spectral method of solving matrix algebraic Riccati equations, Sov. Math. Dokl., v. 35, n. 1, 121–125.
Arnold, U.F., and Laub, A.J., 1985, Generalized eigenproblem algorithms and software for algebraic Riccati equations, Computer-Aided Control Systems Engineering (Ed. by Jamshidi, M.,and Herget,C.J.), B.V., Elsevier Science Publishers, 279–300.
Ikramov,H.D., 1984, Numerical Solving Algebraic Matrix Equations (in Russian), Moscow: Nauka.
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© 1992 Springer Fachmedien Wiesbaden
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Cheremensky, A., Dakev, N. (1992). Matrix “Stable-Unstable” Bloc Triangular and Diagonal Forms. In: Hodnett, F. (eds) Proceedings of the Sixth European Conference on Mathematics in Industry August 27–31, 1991 Limerick. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-09834-8_17
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DOI: https://doi.org/10.1007/978-3-663-09834-8_17
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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