Solution of the $\mathrm H_\infty$-optimization problems on the basis of the principle of separation

A new approach to the design of the central output $\mathrm H_\infty$-controller was proposed. It is based on defining the controller's structure in compliance with the principle of division which is applicable equally to the standard nondegenerate problem and the degenerate problems such as the singular filtration problem (no measurement noise) and singular control problem (no component containing control in the controlled output). Within the framework of the given approach, the general problem of designing the output controller was shown to fall down into two special design problems – under full information and full control. For the degenerate problem, the dimension of the central controller at that drops, and the solution itself is coordinated with the problem of $\mathrm H_2$-optimization. An example illustrating solution of the singular filtration problem was presented, and the results obtained were analyzed.