A new discrete-time stabilizability condition for Linear Parameter-Varying systems

We introduce a new condition for the stabilizability of discrete-time Linear Parameter-Varying (LPV) systems in the form of Linear Matrix Inequalities (LMIs). A distinctive feature of the proposed condition is the ability to handle variation in both the dynamics as well as in the input matrix without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic stabilizability result as a particular case. A numerical example illustrates the results.