On input/output maps for nonlinear systems via continuity in a locally convex topology
نویسندگان
چکیده
In this paper we show that the output of a nonlinear system with inputs in (L2 [0, T]; R ' ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results.
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