If the PM can make great decisions in Matrix organization such as; Generating Project Charter, then it must be Strong Matrix Organization but, it's clear from the question that the organization type is either Week Matrix or balanced Matrix and hence, the PM power will not reach to that level of producing a Project Charter or having it approved.
So, I believe "if this is a real management question!" the PM needs to produce Human resource management plan with clear RAM Stressing on responsibilities, availability of human resources, resource calendar and the reporting structure. The PM should recognize the extent of his power in a Matrix Organization environment.
Getting written commitment on the RAM from the functional managers will reduce the bad effect of duel reporting mechanism.
The bottom line is that, you accept to work in Matrix Organization and it is your Soft skills that will govern your relationship and maximize your power in addition to other skills which might put you in a strong position "power of expert and referent"
Emad Sabri