Normalized problem of anisotropy-based stochastic $\mathcal H_\infty$ optimization for closed-loop system order reduction by balanced truncation

This paper addresses the normalized problem of anisotropy-based stochastic $\mathcal H_\infty$ optimization for a linear discrete time-invariant system. The problem includes the problem of linear-quadratic Gaussian controller design and $\mathcal H_\infty$ optimization problem as limiting particular cases. It is shown that the order of a cross-coupled nonlinear algebraic equation system defining the optimal controller realization matrices can be reduced. This equation system can be partially decoupled that results in its simplification.