Efficient Eigenvalue Assignment for Large Space Structures

A novel and efficient approach for the eigenvalue assignment of large, first-order, time-invariant systems is developed using full-state feedback and output feedback. The full-state feedback approach basically consists of three steps. First, a Schur decomposition is applied to triangularize the state matrix. Second, a series of coordinate rotations (Givens rotations) is used to move the eigenvalue to be reassigned to the end of the diagonal of its Schur form. Third, the eigenvalue is moved to the desired location by a full-state feedback without affecting the remaining eigenvalues. The second and third steps can be repeated until all the assignable eigenvalues are moved to the desired locations. Given the freedom of multiple inputs, the feedback gain matrix is calculated to minimize an objective function composed of a gain matrix norm and/or a robustness index of the closed-loop system. An output feedback approach is also developed using similar procedures as for the full-state feedback wherein the maximum allowable number of eigenvalues may be assigned. Numerical examples are given to demonstrate the feasibility of the proposed approach.