The LQG/LTR procedure for multivariable feedback control design

This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQG/LTR is interpreted as the solution of a specific weighted H²-tradeoff between transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the minimum-phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SISO and certain nonminimum-phase MIMO cases which guides the weight selection process.