Design of dynamic suboptimal low-order controllers on basis of the $\mathrm{H}_\infty$-criterion

A design problem of dynamic reduced-dimension controllers according to the boundedness condition of the $\mathrm{H}_\infty$-norm of a transfer matrix of a closed system is studied. The problem of controller deflation is related to the solution to degenerate filtering problems (no noise of measuring) and to degenerate control problems (no control in a manipulated output). It was demonstrated that these problems can be solved on basis of the modified 2-Riccati approach, in which the “filtrating” (for a singular filtrating problem) or the “control” (for a singular control problem) Lurie–Riccati equations have a low order. An example of an optimal reduced-dimension controller design is given that illustrates the obtained results.