Mean-square synthesis of digital systems via the methods of $H$-theory

The problems of mean-square synthesis are considered on the base of the modern approach to digital LTI systems optimization in the sense of banach spaces norms. It is shown that the optimal mean-square synthesis can be treated as an optimisation problem in $H_2$-space and that $H_{\infty}$ problem is a quite suitable representation of the guaranteeing mean-square synthesis. New spectral methods are proposed to solve these problems without resort to the Riccati equations that provides a convenience for certain spectral features of an optimal controller investigation and essentially simplifies an optimal transfer function design. The ultimate position has distinct significance for the embedded controller adaptive turning for real-time implementation.