Anisotropic suboptimal control of linear discrete time-varying system on finite time horizon

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