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The H2 gain scheduled state feedback problem is considered by using the parameter-dependent Lyapunov function for linear parameter varying system, in which the dependent parameter is assumed to be measurable on-line in a polytope space. First, a new linear matrix inequality (LMI) representation provides a type of H2 cost computation for this system. With the introduction of the extra variable, this condition provides a decoupling between Lyapunov function matrix and system matrices and will be useful for a synthesis problem study. Secondly, using a polytopic characteristic of the dependent parameter, based on this representation gain scheduled state, the feedback synthesis problem can be transformed into finite-dimensional LMIs formulation. In addition, by using the parameter-dependent Lyapunov function, it can reduce the conservatism that occurred before in the H2 performance synthesis problem with a fixed Lyapunov function. Finally, a numerical example is included to illustrate the efficiency of the proposals.