Parametric gain-scheduling control via LPV-stable realization

It has been recently shown that, given a plant described by a parametric transfer function, any compensator that internally stabilizes the plant for each constant value of the parameter can be realized in such a way that the closed-loop stability is guaranteed under arbitrary variations of the parameter (LPV stability), provided that certain necessary and sufficient stabilizability conditions are satisfied. The realization of such an LPV stabilizing compensator is based on the Youla–Kucera parametrization of all stabilizing compensators; precisely, closed-loop LPV-stability can be ensured by taking an LPV-stable realization of the Youla–Kucera parameter. In this chapter, the technique is further explored, and several issues concerning the practical implementation of the control are considered. The applications include pointwise optimality with guaranteed LPV stability, online parameter tuning, and parametric pole assignment. Some design examples are worked out to show the features of the proposed approach.