Interest in the delta operator as a tool in the development of robust approaches to modelling and control has been revived in the last decade, principally following the work of Goodwin (1985). The use of this discrete differential operator provides improved numerical properties particularly when modelling or implementing control at high sampling frequencies or under finite wordlength restraints. The delta operator also provides for the alliance of continuous time designs and discrete time application, linking traditional control theory with modern implementation through digital computing.

In this thesis, a delta operator Simplified Refined Instrumental Variable (SRIV) approach to model estimation is employed, together with model order identification tools, to provide delta operator models for use in control and forecasting. The True Digital Control (TDC) design theory is adopted to develop a delta operator Proportional-Integral-Plus (PIP) controller. The construction of realisable control filters enables implementation of the PIP controller, the structure of which can prove operationally significant. A number of refinements to the standard PIP controller are developed and applications are presented for engineering and environmental examples.

The development of a recursive delta operator Kalman filter is presented and incorporated within a forecasting framework. The resulting algorithm is applied to historical data to generate real time stochastic forecasts of river flows from an effective rainfall-flow model.