For passive infinite-dimensional systems, the LQ optimal cost operator is a contraction; for energy preserving systems it is the identity, with the optimal control being negative output feedback (impedance) or zero input (scattering), under strong stability assumptions.
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LQ optimal control for infinite-dimensional passive systems
For passive infinite-dimensional systems, the LQ optimal cost operator is a contraction; for energy preserving systems it is the identity, with the optimal control being negative output feedback (impedance) or zero input (scattering), under strong stability assumptions.