I have ever done a study about Friction Pendulum System (FPS). If I am not mistaken, the variable that you need to know and consider are:
1. Friction coefficient (Miu)
It depends on the surface material that you use. This factor is the most important factor for friction pendulum isolator which will influence all of the other important behaviour.
2. Radius of curvature
This parameter will influence the natural period of the friction isolator system. You need to consider this parameter carefully when you are designing the isolator in order to avoid the period which resonances with the ground acceleration. In order to lengthen the natural period of the super-structure, what you can do is increase the radius of curvature of the isolator.
3. Initial Stiffness
This value is quite tricky. In the ideal condition, you can assume that initial stiffness is almost infinite because no movement will occur before the force surpasses the weigth of the building x friction coefficient. However, in the real practice and computational model, there will be an initial slip thus you need to determine a value which should be far higher than the post-elastic stiffness to represent the condition properly.
Basically, these 3 factors are the main factors that influence the behavior of FPS. Other parameters can be calculated based on this 3 parameter information. For your information, the horizontal stiffness of the isolator will depend on the radius of curvature, while the yield strength of the isolator depends on the weight x miu. Hope it helps!