On the relation between continuous and discrete nonlinear parametric models

Abstract

Actual applications of system identification and modeling utilize discrete-time (sampled) data and yield discrete-time models, although the actual physical processes subserving the system may occur in continuous time. In the case of nonlinear parametric models, the physical interpretation of the estimated model parameters may change considerably between discrete-time (difference equation) and continuous-time (differential equation) representations. Furthermore, a continuous-time model may be desired, although only discrete-time data are available. Thus methods for defining the equivalence between these two forms of nonlinear parametric models are critically needed to assist in model development and interpretation. This paper presents the ‘kernel invariance method’, which is a conceptual extension of the ‘impulse invariance method’ in linear system modeling, as the means for defining the equivalence between continuous discrete nonlinear models.