In this paper, a class of linear parameter-dependent output feedback controllers that satisfy quadratic stability and an induced L-2-norm bound for a given linear parameter-varying (LPV) plant is considered. By using a parameter-independent common Lyapunov function, the solvability conditions are expressed in terms of finite-dimensional linear matrix inequalities (LMI＇s) evaluated at the extreme points of the admissible parameter set. Conditions under which strictly proper controllers can be used are obtained. By restricting some of the controller matrices to be constant, the input and output matrices can be parameter-varying without destroying the problem＇s convexity. Cases where the controller matrices can be obtained without interpolation are also discussed. thereby simplifying the implementation of the controller. A numerical example is included which demonstrates the application of the results.