A novel Lyapunov stability based method for the parameter space design of linear time invariant control systems is proposed in this paper. The basic idea lies in utilizing the Lyapunov equation as the basic vehicle for mapping the stability bounds into the control parameter space. In comparison to the existing parameter space methods in the literature, the new technique provides two computationally critical advantages. First, it avoids the necessity for the frequency gridding which has been almost traditional and a source of an inherent computational complexity. Second, the proposed design method provides directly the bounds in the multi-dimensional control parameter space, thereby dropping the limitation of most related design techniques that take place on a parameter plane. The usage of the proposed method is demonstrated in the prominent case study of a PID control.