Exact discrete-time modelling of linear analogue systems

The discrete-time minimum variance filtering of continuous-time processes and the duality between the problems of discretized filtering and regulation are considered. The discrete-time optimal filter consists of a digital algorithm which is applied to the prefiltered sampled measurements. This algorithm is based on the overall discretetime equivalent model (i.e. the continuous-time process, the prefilter and the sampler). For the first time, different formulations of this discrete-time equivalent model are presented in a comprehensive unified way. A few prevailing misundzrstandings of the discretization issue are clarified and a few errors that appear in the literature are corrected. The equations that govern the optimal linear quadratic discrete-time regulation of continuous-time systems are presented. By comparing these equations to the equations that have been obtained for the optimal filtering problem we show that the optimal discretized filtering problem is not dual to the corresponding problem of the discretized optimal regulation.