Improved linear matrix inequality conditions for gain scheduling

We consider a linear system whose state-space equations depend rationally on real time-varying parameters, which are positive or bounded. Assuming that every parameter is measured in real-time, a stabilizing, parameter-dependent controller is sought, such that a given L₂-gain bound for the closed-loop system is ensured. Sufficient linear matrix inequality conditions are known, that guarantee the existence of such “gain-scheduled” controllers. We first devise a general result pertaining to control synthesis of a class of linear fractional transformation systems with positive and bounded operators. Using this result, we obtain improved LMI conditions for gain scheduling control. These conditions take into account not only the structure but also the realness of the perturbation. Numerical experiments demonstrate a drastic improvement in the achievable L ₂-gain bound