Loop shifting and non-conservative qLPV design

As an extension of the robust H∞ theory, the time domain design based on linear matrix inequalities (LMI) is a conceptually simple and efficient framework to obtain qLPV controllers. However, the constructed scheduling variables are not always suitable for an efficient implementation. This paper investigates the possibility of constructing the scheduling block of a qLPV controller explicitly, i.e., in the form of a linear fractional transformation (LFT). It is shown here that if both the primary and dual multiplier LMI equations lead to maximal indefinite subspaces and a coupling condition holds, the problem can be solved and a constructive algorithm results to build the desired scheduling variables