Parametric design of output feedback controllers in the frequency domain

A frequency domain parameterization of static output feedback controllers assigning all n closed loop poles to an nth order system with p inputs and m ≥ p outputs under the condition m+p > n is developed. By introducing the set of n closed loop poles and the set of m-1 pole directions as free design parameters, an explicit parametric expression for the constant output feedback gain K_y is obtained. This feedback gain is completely parameterized in a two stage design procedure without constraints on the free parameters. In the first stage m-1 poles and their corresponding m-1 pole directions are assigned. The second stage uses a special left coprirne matrix fraction representation of the output feedback problem for the assignment of the remaining n-m+1 ≤ p closed loop poles. Also in the case n > m+p-1, where not all n closed loop poles can be shifted to desired locations, a simple design procedure is proposed to yield suitable locations for all closed loop poles. Examples illustrate the presented design procedure.