On Intrinsic Lipschitz Constants and Bounds in Nonlinear One-Dimensional Discrete-Time Realizations of Input/Output Maps

This paper examines certain aspects of the realizability of input/output maps f: R* ¿ R by one-dimensional non-linear discrete-time systems, where R* is the free monoid on the reals R, under the operation of string concatenation. Realizations are sought which are bounded and/or Lipschitz. A natural connection between such constrained realizations and the string-processing properties of the input/output mapping is shown to exist. These results have further implication for the synthesis of general analog/digital coders and decoders which find uses in computer control system interfaces.