Robust Eigenstructure Assignment: New Approach

This paper considers the problem of robust eigenstructure assignment, which involves finding a feedback gain matrix that makes the closed-loop system insensitive to perturbations or parameter variations. The main contribution of the paper is to derive a new robustness measure using the matrix perturbation theory. The new measure is used to formulate a new method for robust control of the system via state or output feedback. The freedom provided by eigenvalue assignment of multivariable systems is applied to optimize the new index using genetic algorithms. The new results expressed in this paper confirm the previously derived results on robust eigenstructure assignment. In the case of state feedback design, the new robustness index verifies a previously proposed robustness measure. A numerical example is presented to illustrate the effectiveness of the proposed method.