OPTIMIZATION OF THE LOOP TRANSFER-FUNCTION

In quantitative feedback synthesis, the objective is to satisfy assigned performance tolerances over given ranges of plant uncertainty and external disturbances. In such linear and non-linear problems, whether single, multiple-loop or multivariable, the synthesis techniques result in frequency-domain bounds psi ( omega ) in the complex plane, on the loop transmission functions L//i(j omega ). This paper presents a simple proof that an optimum L//i(j omega ) lies on its psi //i( omega ) for each omega epsilon left bracket 0, infinity ). Also, a numerical technique is presented for deriving any desired approximation to the optimum.