Feedback system design: The pole placement problem

The pole placement problem is studied in, a frequency domain setting in which it is desired to define a feedback compensator which will simultaneously stabilize the system and place the poles of the resultant input-output gain at the zeros of a prescribed Hurwitz polynominal, q(s). In the single variate case this may be achieved if and only if o(q) > = Πp) - δwhere o(q) is the order of q(s), п(p) is the total number of RHP poles and zeros of the plant, and δ is either 1 or 0 while in the multivariate case similar, but only partial, numerical results are obtained. Moreover, when these inequalities are satisfied a complete parameterization of the required set of compensators is obtained.