Spatial discretization and approximation of distributed feedback loops and inputs

The problem of approximating distributed feedback loops and inputs by discrete (in space) ones is studied in some detail. The proof is based on the Fredholm-Hilbert idea for solving integral equations. The main result gives sufficient conditions on the plant, input, and compensator enabling such an approximation. The result is illustrated by two examples. One of them is a heat equation and another is a (damped) wave equation for which boundary value problems are solved.<
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