Static output feedback anisotropic controller design by LMI-based approach: General and special cases

This paper considers an approach to attenuation of uncertain stochastic disturbances for a linear discrete time invariant system. The statistical uncertainty is measured in terms of the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is applied as a performance criterion. The designed anisotropic suboptimal controller is a static output feedback gain which is required to stabilize the closed-loop system and keep its anisotropic norm below a prescribed threshold value. The general static output feedback synthesis procedure implies solving a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities in reciprocal matrices which make the general optimization problem nonconvex. By applying some known standard convexification procedures it is shown that the resulting optimization problem is convex for some specific classes of plants defined by certain structural properties. In the convex cases, the anisotropic γ-optimal controllers can be obtained by minimizing the squared norm threshold value subject to convex constraints. The proposed approach to the anisotropy-based optimization is novel as the static output feedback anisotropic controllers have not been considered before.