Controller scheduling blocks in non-conservative LPV design*

As an extension of the robust H∞ theory, the time domain design based on linear matrix inequalities (LMI) presented in Scherer [2001] is a conceptually simple framework to obtain LPV controllers. However the constructed scheduling variables are not suitable for an efficient implementation, in general. 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 that if both the primary and dual multiplier LMI equations leads to maximal indefinite subspaces and a coupling condition holds, then the problem is solvable. If it is the case, a constructive algorithm was also provided to build the desired scheduling variables.