Let us consider a disturbance attenuation problem for discrete linear time invariant systems. The systems are under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in terms of relative entropy using the mean of anisotropy functional. The disturbance attenuation capabilities of the systems are quantified by the anisotropic norm. It represents a stochastic counterpart of the H∞ norm.

The designed anisotropic suboptimal controller is generally a dynamic fixed-order output-feedback compensator, which is required to stabilize the closed-loop system and keep its anisotropic norm below a prescribed threshold value. The general fixed-order synthesis procedure implies solving a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities in reciprocal matrices. These matrices cause that the general optimi-zation problem is nonconvex. By applying the known standard convexification procedures it is shown that the resulting optimization problem is convex for several cases of specific structure of plant and controller.

In a sense, the anisotropic controller seems to offer a promising and flexible trade-off between H2 and H∞ controllers, which represent its limiting cases.

Ing. Michael Tchaikovsky, CSc.
Laboratory 1, Laboratory of Dynamics of Control Systems
Trapeznikov Institute of Control Sciences
Russian Academy of Sciences
Profsoyuznaya st. 65
117997 Moscow
Russian Federation