  Discrete-time models are very convenient to simulate a nonlinear system on a
computer. In order to build the discrete-time simulation models for the
nonlinear feedback systems (which is a very important class of systems in many
applications) described as y(t) = g1(u(t), y(t)), one has to solve at each time
step a nonlinear algebraic loop for y(t). If a delay is present in the loop,
i.e., y(t) = g2(u(t), y(t -1)), fast recursive simulation models can be
developed and the need to solve the nonlinear differential-algebraic equations
is removed. In this paper, we use the latter to model the nonlinear feedback
system using recursive discrete-time models. Theoretical error bounds for such
kind of approximated models are provided in the case of band-limited signals,
and furthermore, a measurement methodology is proposed for quantifying and
validating the output error bounds experimentally.
