Discrete-to-continuous dynamics reconstruction for bilinear systems

In this work, we study the reconstruction of continuous-time models from discrete-time models of bilinear systems. Many dynamical systems contain nonlinearities and evolve continuously in time. However, due to the use of digital sensors for data acquisition, system identification methods typically rely on sampled data and yield a discrete-time model. Linking such a discrete-time model to its equivalent continuous-time dynamics is nontrivial. This paper proposes a discrete-to-continuous dynamics reconstruction for discrete-time models of a class of bilinear systems obtained by system identification. We show that for bilinear systems we can obtain a discrete-time model that is consistent with the measurement data. Furthermore, we show that one can derive from the discrete-time model, its equivalent continuous-time model. Two examples illustrate the approach.