Synthesis of digital $H_\infty$-controllers for multidimensional systems with given accuracy with the mean squared criterion

We consider linear multidimensional objects subject to power bounded polyharmonic perturbances and measurement noise that contains an arbitrary number of harmonics with unknown amplitudes and frequencies. For such objects, we propose a synthesis method for digital state controllers and controllers with respect to measurable output. The problem of guaranteeing a desired accuracy is formulated as the problem of guaranteeing a given mean squared radius of the stabilized state [1]; our solution of this problem is based on the choice of weight matrices in the minimal quadratic functional of a discrete $H_\infty$-optimization problem. We give a synthesis algorithm for a digital controller in the LMI Control Toolbox package and a numerical example for an interconnected electric drive.