Robust eigenstructure assignment for linear systems with external disturbance

An approach that uses closed-loop controllability and disturbability conditions for the selection of closed-loop eigenstructures is proposed for the design of time-invariant linear systems with disturbance. For this approach, a nonlinear optimization technique is combined with the eigenstructure assignment technique. A performance index expressed in terms of the norm of the weighted controllability elements and the norm of the weighted disturbability elements is defined for the optimal selection of closed-loop eigenvalues and their corresponding reciprocal eigenvectors. The overall system sensitivity to external disturbance is greatly reduced by the proper selection of the weighting factors. The light damping closed-loop eigenvalues and their corresponding reciprocal eigenvectors of modes are chosen to be either decoupled from the external disturbance or have low sensitivity to the disturbance. A necessary and sufficient condition for the assignment of a set of closed-loop eigenvalues and their corresponding reciprocal eigenvectors is also developed