The relationship between the Zames representation and LQG compensators

Recently Zames [1] has introduced the so-called model reference transformation which can be used to conveniently parametrize the class of linear time-invariant multivariable compensators that lead to stable feedback control systems. A very popular design methodology for designing stable and robust multivariable control systems is that based on the Linear-Quadratic-Gaussian (LQG) design methodology with Loop Transfer Recovery (LTR). Thus, it is natural to inquire upon the relationship between the Zames representation and the LQG/LTR compensators. This paper summarizes this relationship.