Diagnosability Test for Nonlinear Systems Using the Characteristic Set

Differential algebra tools have been applied to study the identifiability of dynamic systems described by polynomial or rational equations, but have hardly ever been considered to check the diagnosability of nonlinear systems. The diagnosability here is given by the algebraic observability of the variable modelling the fault. In this note, the differential polynomials defining dynamical systems are considered as the generators of a differential ideal in a differential ring. The characteristic set of this ideal describes the same solution set of the original system. Its special structure allows to construct the exhaustive summary of the model used to test the diagnosability.