On the recovery procedure for LQG systems

Abstract The loop transfer function recovery (LTR) procedure of Doyle and Stein (1979, IEEE Trans. Aut. Control , AC-24 , 607–611) is re-examined in the context of singular measurement LQG systems. Using existing closed form expressions for singular optimal estimation an alternative proof of the LTR is presented. Some of the structural properties of the LTR are obtained naturally using this approach. It is shown that in the limit the control effort becomes infinite and therefore the critical tradeoff is between control effort and robustness.