New Robust Stability and Stabilizability Conditions for Linear Parameter Time Varying polytopic systems

Uncertain Linear Parameter Varying (LPV) systems have a long history of interest in the control community. Those where uncertainties depend on time are more and more treated, for either analysis or design problems. The main issue for large part of them is how to represent the derivative of the time varying parameter. We give in this sense a novel representation of the time derivative of the parameter expressed itself under a polytopic structure. Based on that representation, new sufficient conditions for stability and stabilizability are derived, formulated in terms of LMIs parameterized through a real parameter a. A state feedback synthesis is investigated. The influence of the parameter alpha is highlighted by a numerical example. Its impact on the stabilizability's regions delimited by the plane is illustrated by a diagram at the end of the article.