Anisotropic Balanced Truncation - Application to Reduced-Order Controller Design

This paper addresses the problem of reduced-order normalized anisotropic optimal controller design by anisotropic balanced truncation. This controller is the solution to the normalized anisotropy-based stochastic H-infinity problem. Anisotropic balanced truncation is aimed at reducing the order of closed-loop system. Two respective Riccati equations involved are used to define a set of closed-loop input-output invariants of closed-loop system called anisotropic characteristic values. The part of controller corresponding to smaller anisotropic characteristic values is truncated to give a reduced-order one. Truncation is carried out for the closed-loop state-space realization in anisotropic balanced coordinates, when the product of two respective Riccati equation solutions is a diagonal matrix with the squares of anisotropic characteristic values situated in descending order on its main diagonal. In anisotropic balanced coordinates, small characteristic values correspond to states which are easy to filter and control in a sense of anisotropic norm. It is shown that the reduced-order anisotropic controller is the full-order one for the reduced-order plant.