Chain-scattering description approach to characterise stabilising controllers and optimal H2 solution

This study presents an alternative method for solving a general class of control synthesis problems by employing chain-scattering matrix descriptions and coprime factorisations. Extended from Kimura's approach, the proposed method follows an abridged development without the need for any plant augmentation or the conjugation technique in its solution process. It is shown that general control synthesis problems, including those for stabilising controllers or further for H-2 controllers, can be represented via two associated chain-scattering matrix descriptions and solved by means of two coprime factorisations. In the two-port chain description framework, the coprime factorisation is utilised as the fundamental idea instead of J-spectrum factorisation from the perspective of facilitating the process of guaranteeing no unstable pole-zero cancellation. A significant contribution of this study is its transparency and intuitive nature, providing a systematic theory of control and allowing practicing control engineers to learn this approach more easily and apply it to advanced control systems. Related graphic network representations are also presented to help explain the whole concept which will benefit engineering readers.