Lowering orders of derivatives in non-linear residual generation using realization theory

Consistency relations are often used to design residual generators based on non-linear process models. A main difficulty is that they generally include time differentiated versions of known signals which are difficult to estimate in a noisy environment. The main results of this paper show how to lower the need to estimate derivatives of known signals in order to compute a residual. Necessary and sufficient conditions for lowering the order of the derivatives in one step are presented and a main step in the approach is to obtain a state-space realization of the residual generator. An attractive feature of the approach is that general differential algebraic system descriptions can be handled in the same way as for example ordinary differential equations and also that stability of the residual generator is always guaranteed.