An Approach to Parametrization of Suboptimal Anisotropic Controllers

The problem of parametrization of suboptimal and γ-optimal anisotropic controllers in the form of static state feedback for linear discrete-time invariant systems driven by stochastic disturbances with bounded mean anisotropy is considered. In the controller design problem, the solution is based on applying Finsler lemma to the system of inequalities characterizing the boundedness of the anisotropic norm by some number. The relation of the solution of this problem to the solution of the controller design problem for suboptimal and γ-optimal anisotropic controllers via convex optimization without parametrization is pointed out. An example demonstrating the efficiency of the proposed approach to parametrization of anisotropic controllers is provided.