This paper proposes a new synthesis of a gain scheduling controller. Using the dilation lemma, the synthesis condition is derived in terms of linear matrix inequalities with a line-search parameter, which can be solved numerically. Although previous design methods guarantee control performance for every parameter value, resultant gains tend to be too complicated to be implemented in a real system. In contrast, our method yields simple scheduling laws which are preferable for implementation. Derived scheduling laws are piecewise-linear on scheduling parameters and have fewer grid points than scheduling laws of a previous method. Since the synthesis is based on parameter-dependent Lyapunov functions, simple scheduling laws can be derived without deteriorating the performance of the closed loop system. A numerical example demonstrates the effectiveness of the proposed method.