Positive polynomial matrices for LPV controller synthesis

Positive polynomial matrices and linear matrix inequalities (LMI) can be used to design linear parameter varying (LPV) controllers depending polynomially on the scheduling parameters, and robust to polynomial parametric uncertainty. The salient features of the approach are (a) the ability to design a controller of order and structure fixed a priori; (b) the use of a transfer function, or polynomial modeling framework that bypasses difficulties typically encountered with canonical state-space representations of LPV controllers; (c) the existence of a user-friendly Matlab interface to model this class of LMI problems. The main limitation of the approach is the choice of a nominal, or central characteristic polynomial around which the design is carried out.