Abstract
This paper deals with Linear Parameter Varying polytopic systems (LPV) which is a class of linear systems containing time-varying parameters with unknown behavior. The parameter variation is assumed bounded and known. So, non-quadratic Lyapunov function is used to develop relaxed stability and stabilization conditions for LPV systems. Thus, the proposed stability conditions are formulated as a Linear Matrix Inequality (LMI) efficiently solved via a simple algorithm. Finally, to illustrate the effectiveness of the proposed method, some systems are studied and results are compared with other existing.