On the discretization of single-input single-output bilinear systems

Prompted by the observation that the parameters of a discrete bilinear model structure corresponding to a time invariant continuous bilinear model structure are input dependent quantities, this paper deduces a correction factor that relates the continuous and discrete time models. The correction factor that is obtained analytically is shown to provide an exact discretization. An approximation to the correction factor is also included, which produces a satisfactory discretization provided realistic bounds are placed on the choice of the sampling interval. Building on the developed approach for discretizing a first-order bilinear system, the procedure is extended to the case of higher order systems. The new approach differs from existing schemes in that a discrete time bilinear model structure is retained. With consideration given to a first-order model of a high temperature furnace application, it is shown that the resulting parameter variation is significantly reduced when a bilinear model structure is retained and use is made of the proposed bilinear discretization.