Gain-scheduled control synthesis using dynamic D-Scales

The gain-scheduled controller design problem for linear parameter-varying systems is considered. Parameter dependence in the plant is described in the standard linear fractional form familiar from robust control theory. It is assumed that the parameters take values within known bounds and are slowly time-varying. The controller reflects the structure of parametric dependence of the plant and thus has an LFT structure as well. In contrast to the existing results in the literature, dynamic (frequency-dependent) D-scales are used in obtaining sufficient conditions for robust stability of the closed-loop system in the form of frequency-dependent inequalities. Following the transformation to finite dimensions through the use of the Kalman-Yakubovich-Popov Lemma, the controller matrices are eliminated from the resulting matrix inequalities. The main result of the paper is given in terms of convex linear matrix inequalities for the existence of robustly stabilizing controllers. A numerical example highlights the advantages of frequency dependence in the D-scales.