Abstract
The general approach to solve digital control problems is to approximate them by discrete-time control problems, which consider the system behaviour at the sampling instants only, completely disregarding the inter-sample behaviour. In this paper we consider digital control problems without making any approximations, i.e. we solve problems involving continuous-time criteria taking explicitly into account the inter-sample behaviour, which relaxes the demand for a 'small' sampling time. We solve what we call the digital optimal regulator and tracking problem where the continuous-time system is linear time-varying, and disturbed by additive white noise, and the state information at the sampling instants incomplete, and corrupted by additive white noise. The control is piecewise constant, and the continuous-time criteria are quadratic. Both the regulator and tracking problem turn out to be certainty equivalent. The solutions to both the regulator and tracking problem therefore consist of the well-known discret...
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