Balanced Singular Values for LQG/LTR Design

Multivariable design methods based on robustness results for the linear-quadratic regulator or for the Kalman filter require selection of either state/control weighting matrices or process/measurement noise covariance matrices which yield loop return ratios satisfying user-specified design criteria. Such criteria include disturbance rejection, command following, closed-loop bandwidth, and robustness to unstructured uncertainty. The standard method of achieving this first "balances" the singular values of the return ratio of the design at either zero or infinite frequency. An algorithm is described in this paper for "balancing" these singular values at arbitrary frequencies, providing additional design flexibility.