Notes on fading-memory conditions
In some studies concerning the approximation of nonlinear systems, the concept of a weighting function \(w\) plays a central role. This paper, in which attention is focused on continuous-time cases, directs attention to some interesting properties of systems that have \(\mathbb{R}_+\) fading memory or fading memory. In particular, the author shows that half-line input-output maps that have \(\mathbb{R}_+\) fading memory with respect to some \(w\) in fact have \(\mathbb{R}_+\) fading memory with respect to all such \(w\)'s. And it is shown that a similar proposition holds in a setting concerning Volterra-series approximations for continuous-time systems with inputs and outputs defined on all of \(\mathbb{R}\). It is also shown that, in that setting, fading memory is equivalent to uniform fading memory. Some related results are also described.
scientific article; zbMATH DE number 1925614