Design of prescribed-precision controllers of multivariable systems by root-mean-square criterion on the basis of $LQ$-optimization procedures

A problem of designing the continuous controllers of multivariable linear systems ensuring in the root-mean-square their desired precision in the controlled variables under the action of nonmeasurable, power-bounded polyharmonic determinate exogenous disturbances having unknown amplitudes, frequencies, and number of frequencies was formulated. Conditions were established for solvability of the problem with state controllers (in this case, the disturbances and controls must be applied to the same point) and measurable output controllers (the plant must be minimum phase with the same number of controls and controlled variables) on the basis of the $LQ$-optimization procedures by selecting the weight coefficients of the quadratic optimization functional.