Representations of a linear system. Extension to uncertain systems

The following text is an update of the 2006 article [S 7 130] entitled "Representations of a linear system", written by André FOSSARD and Jean-Marc BIANNIC on the basis of the initial version of Marc CLIQUE and Jean-Charles GILLE's dossier entitled "Representation of a system". All the elements of the 2006 version are retained in this article, which also includes a major new section dedicated to uncertain linear systems. The introduction of uncertainties in the modeling of linear systems is essential, as very often many parameters are poorly known. Rather than manipulating a large number of systems associated with different possible values of these parameters, the aim is to propose a more general formulation in the form of a single system in which all uncertainties are grouped within an uncertain operator whose structure is diagonal in blocks. This type of formulation, known as LFT ("Linear Fractional Transformation"), is particularly well suited to the synthesis of uncertainty-robust control laws and robustness analysis techniques, while also facilitating simulation. The following section, dedicated to software aspects under MATLAB, is expanded to illustrate how to model an uncertain linear system very simply, thanks to the definition of a dedicated "object". Finally, the bibliography is updated with several references specific to LFT modeling.