Direct and indirect continuous-time identification in dynamic networks

Many systems can be modelled as networks of interconnected continuous-time transfer functions. The coefficients of the transfer functions in the network are often directly related to physical properties of the system. Thus, the question we consider is: under what conditions is it possible to obtain a consistent estimate of a continuous-time transfer function embedded in a dynamic network? We consider both direct and indirect continuous-time approaches. We show that a discrete-time model of a continuous-time data generating system may have a different interconnection structure (due to aliasing) and may have algebraic loops (due to the intersample behaviour). Subsequently we present an instrumental variable based method to directly identify a continuous-time transfer function embedded in a network.