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Anisotropic ε-optimal model reduction for linear discrete time-invariant system

  • Adaptive and Robust Systems
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Abstract

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 2 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.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    M. M. Tchaikovsky

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Original Russian Text © M.M. Tchaikovsky, 2010, published in Avtomatika i Telemekhanika, 2010, No. 12, pp. 86–110.

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Tchaikovsky, M.M. Anisotropic ε-optimal model reduction for linear discrete time-invariant system. Autom Remote Control 71, 2573–2594 (2010). https://doi.org/10.1134/S0005117910120076

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