Multichannel synthesis problems for anisotropic control

This paper considers a problem of attenuation of uncertain stochastic disturbances exciting a linear discrete time-invariant system. The system's abilities to attenuate the external disturbances are quantitatively characterized by its anisotropic norm. The anisotropic control problem is solved for a standard plant with several groups of channels from the external disturbance inputs to the controlled outputs. These channels have different levels of statistic uncertainty measured in terms of the mean anisotropy. The considered technique also allows to design the anisotropic controllers that ensure the closed-loop poles to be placed in some given convex region of the complex plain.