Eigenstructure assignment and robust stable perturbation bounds of optimal control system

An effective method which assigns the closed-loop eigenvalues of linear quadratic (LQ) optimal control system in desired stable locations and which simultaneously selects those eigenvectors which satisfy a quadratic cost criterion with suitable weighting matrices is presented. The optimal feedback gain matrix is determined by means of a recursive method. Meanwhile, a robustness measure bound is introduced for this LQ state-feedback designs in the presence of perturbations, and bounds are obtained for allowable perturbations so that the resulting closed-loop system remains stable