Probability that an unknown system corresponds to one of two possible systems

#1
My problem can be stated as follows: given two different systems S1 and S2, each characterized by a set of parameters, say {p1,p2,...,pN}, what's a reliable method for determining whether an unknown system Sx corresponds (with a given probability) to S1 or S2?. More precisely, I've already obtained many samples of both systems and carried out a set of measurements for each parameter (i.e. {p11,p12,...,p1m} for parameter p1 of both systems, {p21,p22,...,p2m} for parameter p2 and so on, where the m different measurements correspond to different samples of the same system). Now, I have an unknown system and I measure the parameters. I would like to determine the probability that this system corresponds to S1 or S2.

I don't need a concrete and detailed answer. If someone could give me the name of some technique, method or similar, I can search for more information. My problem is that I don't know where to start looking (I think that this would correspond to some topic of machine learning, but I'm not sure).

Thanks in advance!