Approach to partial eigenvalue assignment using Sylvester equation in system-second order

The article considers an approach for partial eigenvalue assignment in singular second order systems via proportional controller plus derived control plus output feedback controller. It is shown that the problem is closely related to a so-called second-order Sylvester matrix equation. This study presents an approach to partial the eigenstructure assignment for the descriptor system where an algorithm is presented for calculated the output feedback matrix by Sylvester equation. The paper is proposed two complete parametric methods for an approach to partial eigenstructure assignment problems. Both methods are respectively given simples complete parametric expressions for feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions. The second one utilizes methodology for the system's factorization and enables the closed-loop eigenvalues to be set undetermined and search via specific optimization procedures. The theorems are presented using the Sylvester equations. Two algorithms are implemented using the Sylvester equation, and examples are presented with their conclusions.