Optimal and suboptimal digital controllers are developed for the control of a linear, oil-fired boiler model specified by discrete state variables and transition functions.The model is based on design and steady-state test data and the resulting equations are transformed into a normal co-ordinate reference frame for isolating the time-dependent modes of the system. Analytical techniques are developed for reducing the system order, and the open-loop behaviour of the reduced system is shown to be similar to that of the original system.Controller design is based upon measurement and subsequent minimisation of a quadratic performance index related to the displacement of the discrete state variables.For suboptimal control, minimisation is considered at each successive forward sampling point with input amplitude constraints, and this is shown to produce an approximately time-optimal system. The concepts of dynamic programming are used for investigation of the optimal controller. This requires a complex iteration procedure, and the response of the controlled system does not appear to be superior to that of the simplified suboptimal system.The use of Lyapunov functions in the performance index are also investigated, and these are shown to produce local stability of the controlled system.