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On the generalized Sylvester mapping and matrix equations. (English) Zbl 1129.93018

Summary: General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the so-called generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great convenience to the computation and analysis of the solutions to this family of equations, and can perform important functions in many analysis and design problems in linear system theory. It is also expected that this so-called generalized Sylvester mapping tool may have some other applications in control system theory.

MSC:

93B55 Pole and zero placement problems
93B07 Observability
93C05 Linear systems in control theory
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