Accuracy bounds for the simulation of a class of continuous-time nonlinear models

Real-world dynamic systems evolve in the continuous-time world, while their models are simulated in the digital world using discrete-time numerical simulation algorithms. Such simulation is essential for a variety of system and control problems such as system identification and performance analysis of (control) systems. Ideally, the simulated model response should be identical to the system response. However, this is typically not the case in practice, even when the effects of unmodelled dynamics and parametric uncertainty are excluded. Even in that scenario, a mismatch exists between the response of the system and the model due to the interface between the physical world and the digital computer, unknown disturbances, and simulation inaccuracies. For the class of continuous-time, nonlinear Lur'e-type systems, this paper analyses the mismatch between the steady-state system response and the steady-state model response computed using the so-called mixed time–frequency algorithm. Firstly, a bound on the mismatch between the steady-state system response and the computed steady-state model response based on continuous-time signals is derived. Secondly, a bound for the same mismatch is derived for a sampled version of the signals. The bounds are further decomposed into several components, each given an interpretation that can be used to reduce the bounds on the mismatch. In a numerical case study, we show that reducing the bounds also reduces the actual mismatch.