Controllers design via given oscillation index: parametric uncertainty and power-bounded external disturbances

The problem is considered of output controllers design for linear multivariable systems with deviating in prescribed bounds physical parameters of the plant, and subjected to the influence of unknown polyharmonic external disturbances, limited only in power. The controller is built so that to provide the prescribed bounds of mean-square values of controlled variables in addition to the robust stability of the closed-loop system. The problem solution is reduced to the $H_\infty$-optimization procedure produced in some specific way.The solution of the well-known “benchmark” problem is considered.