Improved LMI-based conditions for quadratic stabilization of LPV systems

This paper is concerned with quadratic stabilization problem of linear parameter varying (LPV) systems, where arbitrary time-varying dependent parameters are belonging to a polytope. It provides improved linear matrix inequality (LMI)-based conditions to compute a gain-scheduling state-feedback gain that makes closed-loop system quadratically stable. The proposed conditions, based on the philosophy of Polyapsilas Theorem and on the systematic construction of homogeneous polynomial solution for parameter-dependent LMI, are written as a sequence of progressively less and less conservative LMI. More importantly, by adding an additional decision variable, at each step, these new conditions provide less conservative or at least the same results than previous methods in the literature. Finally, a simple numerical example is given to illustrate the effectiveness of the proposals.