Design of digital state $H_\infty$-controllers of the mimo systems with prescribed precision

For the linear MIMO plants subject to polyharmonic perturbations, a method of designing digital state controllers was developed with regard for the requirements on limitedness of the control actions in the stable state as well as on limitedness of the controlled variables. A notion of radius of the stable state of a closed-loop system was introduced, and the problem of using the full state vector to design a discrete controller providing the desired radius was formulated. Its necessary and sufficient solvability conditions were obtained using the procedure of $H_{\infty}$-optimization by selecting the weight matrices of the discrete Lur'e–Riccati equation.