Schur method for robust partial quadratic eigenvalue assignment problem

A new method is proposed for robust partial quadratic eigenvalue assignment problem (RPQEAP). We first derive an expression of the solution to partial quadratic eigenvalue assignment problem, which yields Schur decomposition associated with quadratic closed-loop system. Then normality departure is used to measure the robustness of quadratic closed-loop system. On these grounds, our method is proposed for RPQEAP such that the normality departure is as small as possible. The proposed method is effective either for distinct prescribed eigenvalues or for repeated prescribed eigenvalues. It directly deals with quadratic control system and avoids the linearization of quadratic eigenproblem. Moreover, our method does not need the unchanged eigenpairs of the open-loop system and the inversion of mass matrix M.