About the loss of robustness of the LQG/LTR compensator

It is known that the optimal LQR regulator (Linear Quadratic Regulator) with full state feedback has remarkable robustness properties, defined by gain margins of (1/2, ) and phase of at least ± 60 degrees. Representing a realistic approach to control synthesis, LQG (Linear Quadratic Gaussian) synthesis elegantly overcomes the difficulties of an unrealistic full output feedback synthesis LQR. LQG synthesis replaces the ideal case of complete feedback after the state by introducing a special, dynamic observer, the optimal Kalman estimator. LQG synthesis is considered the most powerful acquisition of automatic control science (i.e., control with feedback) which has a history of over 85 years. Unfortunately, LQG synthesis is not infallible either. In a famous article, John Doyle demonstrates that the LQG controller cannot guarantee any stability reserve. To counteract this shortcoming, thus appears the LQG/LTR method (Linear Gaussian Quadratic synthesis with Loop Transfer Recovery), in which the shape of the loop of the robust controller with full feedback after state LQR is restored/recovered, via certain specific procedures. This article shows that the LQG/LTR methodology can also lose its robustness. Therefore, our paper reveals a veritable dialectic of challenges: from LQR to LQG, from LQG to LQG/LTR, from LQG/LTR in search of a new, more efficient approach.