Exact discretisation of a scalar differential Riccati equation with constant parameters

An exact, first-order, discrete-time model that gives correct values at the sampling instants for any sampling interval is derived for a nonlinear system whose dynamics are governed by a scalar Riccati differential equation with constant parameters. The model is derived by transforming the given differential equation into a stable linear form to which the invariant discretisation is applied. This is in contrast with other existing methods which result in a second-order and usually unstable form and which is not suitable for on-line digital control purposes. Simulation results are presented to show that the proposed method is always exact at the sampling instants, whereas the popular forward difference model can be divergent unless the sampling interval is sufficiently small.