When continuous-time Gain-Scheduled Output Feedback (GSOF) controllers are designed via Parameter-Dependent Lya-punov Functions (PDLFs), the GSOF controllers, in general, depend on not only the current scheduling parameters but also the derivatives of scheduling parameters. However, it is obvious that the derivatives of scheduling parameters are not available in real world; that is, the designed GSOF controllers cannot be implemented to practical systems. We therefore address the design problem of GSOF controllers via PDLFs while causality of scheduling parameters in GSOF controllers is kept. For this problem, we propose a new formulation in which the causality of scheduling parameters is kept by over-bounding the term causing the causality problem. It is also shown that our method is no more conservative than an existing method in the literature. A numerical example is included to demonstrate the usefulness and effectiveness of our method.