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- Title
Solutions to the matrix equation X − AXB = CY+R and its application.
- Authors
Song, Caiqin; Chen, Guoliang
- Abstract
The solution of the nonhomogeneous Yakubovich matrix equation <named-content> X − AXB = CY + R </named-content> is important in stability analysis and controller design in linear systems. The nonhomogeneous Yakubovich matrix equation <named-content> X − AXB = CY + R </named-content>, which contains the well-known Kalman–Yakubovich matrix equation and the general discrete Lyapunov matrix equation as special cases, is investigated in this paper. Closed-form solutions to the nonhomogeneous Yakubovich matrix equation are presented using the Smith normal form reduction. Its equivalent form is provided. Compared with the existing method, the method presented in this paper has no limit to the dimensions of an unknown matrix. The present method is suitable for any unknown matrix, not only low-dimensional unknown matrices, but also high-dimensional unknown matrices. As an application, parametric pole assignment for descriptor linear systems by PD feedback is considered.
- Subjects
MATRICES (Mathematics); KALMAN-Yakubovich-Popov lemma; STABILITY of linear systems; LYAPUNOV stability; FEEDBACK control systems
- Publication
Transactions of the Institute of Measurement & Control, 2018, Vol 40, Issue 3, p995
- ISSN
0142-3312
- Publication type
Article
- DOI
10.1177/0142331216673422