@mmcdara 

Thank you very much for your reply. I didn't know about the events option before.

The file that I shared above is an example. I tried to apply the two methods you shared with the system I'm working on which must be solved using "mebdfi" (I cannot get any results using any other methods). However, I'm getting an error for both methods:

Using the first method I'm getting:

Error, (in dsolve/numeric) parametrized DAE problems cannot be solved with the 'mebdfi' method.

Using the second method I'm getting the same error:

Error, (in dsolve/numeric) problems with discrete variables cannot be solved with the 'mebdfi' method.

Is there a way to apply those methods for systems the must be solved using "mebdfi" numerical method.

Again, thank you very much for your assistance. I'm sure that I would have run in the future into something similar and your approach is very smart so I will keep it in mind.