Optimal pole assignment of linear systems by the Sylvester matrix equations. (English) Zbl 1406.93134

Summary: The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.


93B55 Pole and zero placement problems
93C05 Linear systems in control theory
93B52 Feedback control
93B25 Algebraic methods
Full Text: DOI


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