Minimal order polynomial discrete-time SISO H2 and H∞ controller synthesis: summary of the results and existence of solution

In a series of recent papers, on the basis of a novel algebraic reduction technique, a new methodology for the computation of the polynomial discrete-time SISO H₂ and H_∞ controllers has been derived and shown to yield minimal order controllers. However, the existence of the H_∞ controller solution has not been addressed. The present paper summarizes the results and presents a method of addressing the existence problem.