Synthesis of optimal robust $H^{\infty}$-control by convex optimization methods

It is shown that the synthesis of robust $H^{\infty}$-control with respect to the output for systems with unknown limited parameters reduces to the solution of an optimization problem under constraints prescribed by a system of linear matrix inequalities. For this kind of problems, an optimization algorithm implemented with the use of standard procedures of the MATLAB package is suggested. The algorithm effectiveness is illustrated by the example of an optimal dampening of vibrations of a parametrically perturbed pendulum.