We consider an ϵ‐optimal model reduction problem for a linear discrete time‐invariant system, where the anisotropic norm of reduction error transfer function is used as a performance criterion. For solving the main problem, we state and solve an auxiliary problem of H
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ϵ‐optimal reduction of a weighted linear discrete time system. A sufficient optimality condition defining a solution to the anisotropic ϵ‐optimal model reduction problem has the form of a system of cross‐coupled nonlinear matrix algebraic equations including a Riccati equation, four Lyapunov equations, and five special‐type nonlinear equations. The proposed approach to solving the problem ensures stability of the reduced model without any additional technical assumptions. The reduced‐order model approximates the steady‐state behavior of the full‐order system.
