Synthesis of anisotropic controllers via convex optimization and semidefinite programming

This paper presents several statements and solutions of the anisotropic suboptimal and $\gamma$-optimal controller synthesis problems for suppression of impact of random disturbances with unknown distributions on a control system performance. The problems of anisotropic controllers synthesis in form of static state feedback, of full-order dynamic output feedback, as well as of static output feedback are considered. Application of standard linearizing changes of variables and known convexification procedures to the synthesis problems for the considered special cases of the plant and the controller structure allow the problem solution to be expressed via a system of convex constraints representable by a system of linear matrix inequalities. The anisotropic suboptimal controller stabilizes the closed-loop system and keeps its anisotropic norm below a prescribed threshold value. The developed optimization-based approach to anisotropic controllers synthesis is novel and more convenient for practical computations.