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A quadratic L2 gain performance LPV control system has been designed using a linear time invariant (LTI) output feedback controller with an iterative linear matrix inequality (ILMI) algorithm. A linear parameter varying (LPV) plant is assumed with immeasurable dependent parameter, which varies in a plant parameter space that is a polytope. Different from gain scheduled LPV control, this is a complex control problem with the non-convex constraint that the controller gain matrix is the same for each vertex plant of the LPV system. To solve this control problem, a heuristic iterative algorithm is presented in the form of a linear matrix inequality (LMI) formulation. An effective method of setting an initial value to the ILMI algorithm proposed here promotes convergence to an admissible solution.