A constrained optimal control problem

In this note the problem of optimizing a standard quadratic cost functional subject to a hard constraint is solved (i.e., the poles of the resulting system must lie in a specified region of the left-half
s
-plane). This can he viewed as a generalization of the problem of finding the optimal controller that yields a system with specified relative stability. The problem is phrased in terms of a design procedure using coprime fractional representations.