Abstract:
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.
Keywords:discrete linear time invariant systems, random
disturbances, statistical uncertainty, norm, anisotropy, convex
optimization, linear matrix inequalities.
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