Anisotropy-Based Approximation of Linear Discrete Time-Invariant Stochastic System
This paper represents an approach to approximative model reduction with anisotropic norm of approximation error as performance criterion. The anisotropic norm of a linear discrete time-invariant system is defined as its worst-case sensitivity to a stochastic Gaussian external disturbance with mean anisotropy
not exceeding some known value. The mean anisotropy of a vector Gaussian sequence quantifies its temporal colouredness and spatial non-roundness. To solve the main problem, an auxiliary problem of weighted H2 near-optimal model approximation is stated and solved. Optimality conditions defining a solution to the anisotropy-based optimal approximation problem are expressed in form of a nonlinear matrix algebraic equation system. The presented approach guarantees stability of the obtained reduced-order model without any technical assumption. The reduced-order model approximates steady-state behaviour of the full-order system.