An energetic approach is presented for the synthesis of polytopic fault observers for a class of discrete-time linear systems subject to multiplicative and additive faults. The main purpose of the proposed approach is to estimate the multiplicative component faults. The direct influence of fault occurrences on the system stability is considered in the design procedure. In the proposed approach, the unknown input-decoupling principle is used to decouple the component faults from sensor and actuator faults. Then, an algebraic technique is used to derive a regressor description of the system energy balance, where the regressor coefficients are component of the fault matrix elements. This formulation provides the possibility of using a Least-Squares technique to on-line component faults estimation. In order to estimate the component fault along with sensor faults, a new observer structure is proposed where the regressor description is coupled with the Unknown Input Observer by means of an auxiliary output

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