Uniform approximation of discrete-space multidimensional myopic maps
It is a known fact that most remarkable results in systems theory are derived for the class of linear time invariant systems (LTIS). The elements of this class may be analogous (i.e. LATIS) or discrete (LDTIS). Beyond this class, the general results are in most cases of particular interest. On the other hand, in the class of nonlinear systems, remarkable results are derived for memoryless ones only. The present paper provides a fundamental result: under sufficiently large conditions, vector-valued discrete-time nonlinear time invariant mappings can be uniformly approximated by a preprocessing element (LDTIS element) followed by a memoryless nonlinear element. The result is derived via an elegantly refined mathematical way. It would perhaps be of interest to give an example illustrating the developed theory.
scientific article; zbMATH DE number 1046381
scientific article