7. Extension to uncertain systems: LFT modeling

In the foregoing, the matrices A, B, C, D of the state representation have all been assumed to be well known. However, this is rarely the case in practice, as these matrices generally depend on uncertain parameters for a variety of reasons. This leads to the manipulation of a large number (or even an infinite number) of representations associated with the various possible parametric combinations. To avoid this complexity, a specific representation is proposed here. It is based on the notion of Linear Fractional Transformations (LFT) and is therefore referred to as an LFT model or representation. A simple introduction is given in this section, based on a graphical illustration of a second-order model.