Synthesis of multivariable systems according to engineering quality criteria based on $H_\infty$-optimization

We solve the output controller synthesis problem for multivariable systems, guaranteeing the following parameters, either predefined or achievable: control errors, stability margin radius, and control time under the action of polyharmonic external disturbances with unknown amplitudes (with a limit on their sum), frequencies, and an unbounded number of harmonics. Our approach to solving the problem is based on a specially designed standard $H_\infty$-optimization problem and a new rule for choosing a weight matrix for a given accuracy. For the first time, we give a physical interpretation of the stability margin radius of multivariable systems in terms of Nyquist hodographs for individual contours that are open at the output of the plant. We prove a connection between the absolute stability property of a closed-loop system and the radius of stability margin. We consider the example of synthesis for an interconnected electric drive.