This paper is concerned with the study of observability in a structured framework. It turns out that the system is structurally observable if and only if the system is output connected and contains no contraction. We focus our attention on the observability preservation under sensor failure. We consider linear observable systems and we wonder if a given system remains observable in case of sensor failure. More precisely we will characterize among the sensors those which are critical and which failure leads to observability loss, those which are useless for observability purpose and the set of those which are useful without being critical. Using a graph approach we classify the sensors with respect to their importance for output connection preservation, contraction avoidance and then observability preservation under sensor failure.• the edge set is W c = {(v i , y j )| when there exists a path from I i to y j } ∪ {(y j , z) for any j}.

This paper is concerned with the study of observability in a structured framework. It turns out that the system is structurally observable if and only if the system is output connected and contains no contraction. We focus our attention on the observability preservation under sensor failure. We consider linear observable systems and we wonder if a given system remains observable in case of sensor failure. More precisely we will characterize among the sensors those which are critical and which failure leads to observability loss, those which are useless for observability purpose and the set of those which are useful without being critical. Using a graph approach we classify the sensors with respect to their importance for output connection preservation, contraction avoidance and then observability preservation under sensor failure.

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International audienceThis paper addresses the sensor classification problem for fault detection and isolation (FDI) with observability requirement in a structural way. The system under consideration is a linear system subject to additive faults and affected by unknown input disturbances. This system is equipped with a sensor network subject to sensor failures. We represent the dynamics of the system by a linear parameterized state space model called linear structured model. The underlying prior knowledge on the system is reduced to the existence or non-existence of relations between variables in the model. A dedicated residual set using a bank of observers is designed in order to detect and isolate the faults. The failure of some sensors may affect the observability of the system which is a natural requirement in order to build stable observers and also may affect the FDI solvability. The main contribution of this paper is to classify the sensors with respect to their importance in case of failure relatively to the considered FDI problem. More precisely, we characterize the sensors that are essential i.e. whose failure leads to FDI solvability loss and those which are useless for such property. We also quantify the relative importance of the sensors which are not useless. The proposed graph approach is visual, easy to handle and close to the physical structure of the system. It is well adapted to large-scale systems and essentially leads to polynomial algorithms here

In this paper, we consider dynamical models and we study the preservation of solvability for the Disturbance Rejection by Measurement Feedback (DRMF) problem under sensor failure in a structural framework. We consider a linear structured system and we wonder if the DRMF problem remains solvable in case of some sensor failure. More precisely we will characterize among the sensors some of those which are critical i.e. which failure leads to solvability loss, and some of those which are useless for solvability purpose.