Polynomial discrete-time SISO H2 and H∞ controller synthesis: single Diophantine equation solution

Is solving a single Diophantine equation sufficient for synthesizing a polynomial discrete-time single-input-single-output (SISO) H_∞ controller? This has been a longstanding question practically important due to the pervasive use of the polynomial-based discrete-time SISO self-tuners. The present work gives the answer to this question through the development of a novel polynomial algebra based reduction methodology. This reduction technique is also applied to the discrete-time SISO polynomial H₂ controller computation.