Synthesis of anisotropic suboptimal control for linear time-varying systems on finite time horizon

This paper presents the statement and solution to the problem of synthesis of the anisotropic control that guarantees some prescribed level of attenuation of the uncertain stochastic disturbances affecting the linear discrete time-varying system on finite time horizon. The anisotropy of a random vector is considered as a measure of the statistical uncertainty of the disturbance. The closed-loop system capabilities to attenuate the external disturbances are characterized by its anisotropic norm. The synthesis problem solution is formulated in form of sufficient conditions of existence of a controller that guarantees the anisotropic norm of the closed-loop system to be bounded by some given threshold level. The controller synthesis algorithm is based on solving the system of matrix inequalities recursively.