This paper presents a new approach to the task of time-domain model matching for state-space systems. The traditional problem formulation of designing a controller to match a reference model is relaxed to matching only a desired reference response. The presented algorithm then computes the feedback gain that delivers the best fit solution to the reference response under general norms. Additionally, the proposed discretization approach enables the employment of sparse matrix methods which enables a numerically efficient implementation. The new method is successfully verified using a random system. Additionally, an application example involving a simplified gantry crane system is presented, showcasing the practicality of the approach. Overall, the new method provides an intuitive and numerically efficient solution to the problem of time-domain model matching for state-space systems.