This is an author's version published in: http://oatao.univ-toulouse.fr/23980 To cite this version:Sakhraoui, Imane and Trajin, Baptiste and Rotella, Frédéric Design procedure for linear unknown input functional observers. (2019) IEEE Transactions on Automatic Control. 1.Abstract-This paper considers an iterative procedure to design a minimum possible order unknown input functional observer for linear time-invariant (LTI) systems. Necessary and sufficient conditions for the existence of the observer are given. The proposed procedure is simple and is based neither on the solution of a generalized Sylvester equation nor canonical forms. This procedure can be easily implemented due to its incremental form. The main feature of our procedure is then the simplicity of the design. Moreover, in the case of a single functional to be observed, a minimum order stable linear unknown input functional observer is obtained.Index Terms-Linear systems, time-invariant systems, unknown input functional observers.

High integrated power electronic modules are designed with the emergence of new semiconductor technologies. The increase of reliability of power modules induces the precise knowledge of the local temperature, even if it can not be measured at any location. In this paper, the application of an observer in the discrete time framework is proposed. It allows to estimate the temperature at any location using measurements provided from thermal sensors located at a few precise points. The aim is to design a reduced size observer that could be implemented on a real-time embedded target such as Digital Signal Processor. Consequently, this works pays attention on the design procedure and the computation complexity of the resulting observer.

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