Anisotropy-Based Approximation of Linear Discrete Time-Invariant Stochastic System
Alexander P. Kurdyukov, Michael M. Tchaikovsky
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.