On representation and approximation of nonlinear systems

Palm, G

doi:10.1007/BF00344243

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On representation and approximation of nonlinear systems

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Palm, G
Former Department Structure and Function of Natural Nerve-Net , Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://link.springer.com/content/pdf/10.1007/BF00344243.pdf
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Palm, G. (1978). On representation and approximation of nonlinear systems. Biological Cybernetics, 31(2), 119-124. doi:10.1007/BF00344243.

Cite as: https://hdl.handle.net/21.11116/0000-0006-8205-1

Abstract

Many methods for the analysis of nonlinear systems rely on a Volterra system-representation in terms of integral kernels. This paper considers two questions: 1) whether Volterra-like representations are possible for all smooth systems (i.e. analytic operators),-2) which classes of systems can be approximated by some interesting subclasses of the smooth systems, e.g. Volterra systems with separable kernels and “sandwich systems” (cascades of linear systems and nomemory nonlinearities). Whereas the answer to question 1 is positive, the answer to question 2 depends on the type of approximation, i.e. topology, that is used.