Synthesis of multidimensional systems of prescribed accuracy by the mean-square criterion

A problem is stated for the synthesis of a continuous controller which ensu res the required accuracy according to controllable variables in the mean-s quare sense under the action of nonmeasurable bounded polyharmonic (externa l) disturbances and measurement noise with unknown amplitudes and frequenci es. Account is taken of the requirements for the boundedness of mean-square control values. The concept of a mean-square radius of the steady state of a closed-loop system is introduced, and a problem is set out for the synth esis of a controller which affords the preassigned radius. The necessary an d sufficient conditions of the problem solvability are found on the basis o f procedures of the H-infinity-suboptimal control by way of the choice of a structure and weight factors of the quadratic optimization functional of t he requisite minimax problem.