$H_\infty$-approach to controller synthesis under parametric uncertainty and polyharmonic external disturbances

We consider the robust stabilization problem for linear multivariable systems whose physical parameters may deviate from computed (nominal) in some known bounds, and the control object is subject to non-measurable polyharmonic external disturbances (with unknown amplitudes and frequencies) bounded in power. We pose the problem of synthesizing a controller that guarantees robust stability of the closed-loop system and additionally ensures given errors with respect to controlled variables in the established nominal mode. The solution of this problem is based on the technique of opening the object-controller system with respect to varying object parameters and can be reduced to a standard $H_\infty$-optimization procedure, while the necessary accuracy is achieved by choosing the weight matrix for controlled object variables. We show the solution for a well-known benchmark problem.