Parametric Jordan Form Assignment Revisited

Abstract

AbstractThe Jordan form assignment problem (complete and partial) for linear multivariable control system is formulated and completely solved by the unified Sylvester matrix equation approach. A new explicit parametrization of all state feedbacks assigning an admissible Jordan form through the minimum number of parameters is provided. The main advantage of this parametrization, unlike previous ones, is that it is explicit; thus, it can be used, not only for numeric, but also symbolic computations. This fact is demonstrated on the problem of parametrization of all output feedbacks assigning an admissible Jordan form, where Gröbner basis method is applied. Developed algorithms for Jordan form assignment by state and output feedback are implemented in the freely available Maple package.