Minimum norm partial eigenstructure assignment problems in high-order system via feedback control

In this article, the minimum norm partial eigenstructure assignment problem (MNPESAP) is considered in a symmetric high-order system using feedback control law with the highest-order derivative term. Two new orthogonality relations are constructed using the system matrices and undetermined feedback gains. The parametric expressions of the feedback controller and the necessary and sufficient condition for solving the partial eigenstructure assignment problem are derived. The Sylvester matrix equations and gradient formula are presented for solving MNPESAP. An algorithm is proposed to obtain the minimum norm solutions of feedback gains using gradient-based optimization method. Numerical examples are provided to verify the effectiveness of given results.