1. Solution of the Spectrum Allocation Problem for a Linear Control System with Closed Feedback.
- Author
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Zubova, S. P. and Raetskaya, E. V.
- Subjects
- *
LINEAR dynamical systems , *FEEDBACK control systems , *POLE assignment , *SPECTRUM allocation , *DECOMPOSITION method , *CONTROLLABILITY in systems engineering , *LINEAR control systems - Abstract
A method for constructing a feedback matrix to solve the spectrum allocation (spectrum control; pole assignment) problem for a linear dynamical system is given. A new proof of the well-known theorem about the connection between the complete controllability of a dynamical system and the existence of a feedback matrix is formed in the process of constructing the cascade decomposition method. The entire set of arbitrary elements affecting the nonuniqueness of the matrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum and in the presence of complex conjugate eigenvalues as well as for the case of multiple eigenvalues are given. The stability of the specified spectrum under small perturbations of system parameters with a fixed feedback matrix is studied. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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