On an algebraic and differential approach of nonlinear systems diagnosis

We proposed previously (2001) a new approach of systems diagnosis which consists of viewing the ability to detect, identify and estimate the fault variable as an observation problem of the latter variable with respect to the input and output online data. Once a fault component is recognized as "diagnosable", i.e., observable, we then propose an estimation scheme which mainly relies on data numerical differentiation. In this paper some of the main points of this approach are further discussed. First, the fact that "diagnosability" is the condition one would ideally need to virtually completely solve the fault detection, identification and estimation problem is exemplified. Next, we discuss the point that a system may be "diagnosable" without being observable. In that case we cannot simply use standard observers to design the so-called detection filters. Next, we provide further comments on a question that one may ask about the interrelation between practical differentiation schemes and the potential presence of uncertainties in the system dynamics. Finally we further illustrate the approach through two simple nonlinear examples.