Synthesis of regulators in a control problem with the generalized $\mathrm H^{\infty}$-criterion

An issue of synthesis of linear regulators is considered, which involves a control problem with a generalized $\mathrm H^{\infty}$-criterion that makes it possible to smooth out values of the maximum coefficient of attenuation of the vibrational energy. An effective theorem of existence of the desired solution is proved. An example is given.