Frequency weighted controller reduction methods and loop transfer recovery

This paper shows that if one designs an LQG system by combining the reduced order controlcontroller using the conventional technique of loop transfer ler and the high order therefore, it is quite recovery (LTR), then two frequency weighted controller reduction methods, the Enns' frequency weighted balanced that in truncation (Enns, 1984a, Ph.D. Thesis, Stanford University, problems, one should take into account the CA; 1984b. Proc. 23rd CDC, Las Vegas, NV, 127-132) and of the plant in the controller reduction the Bezout identity induced frequency weighted reduction method (Anderson and Liu, 1987, Proc. Arner. Control procedure itself, Or, put way, the C o d . MN) will be equivalent under the condition that the reduction mocedure should be based on , . . plant transfer function is square, nonsingular and minimum phase. We also show that Enns' method is equivalent to the Bezout identity induced frequency weighted reduction method if the controller itself is stable and a particular representation far the controller is assumed.