Sure

As @TRomano already linked before denying his own research, plenty of people use the expression 'perform control(s)'.

Neither of you is wrong that the expression seems odd. The most common sense of control as a noun is the interface used to direct the actions of some device. The original sense was as a synonym for restraint or for a means of restraint. Perform doesn't work for any of those: apply is what happens to restraint and use is more common than either of them.

That said, the phrase in question shows up at ngram because other definitions of control exist. Its scientific sense as an experiment performed without a certain variable or factor is imminently performable. Its general sense as direction, management, or administration and its senses as a clipped form of control group, animal, &c. both suggest roles which can be performed.

More importantly, the original quote is not about 'controls' generally but about 'in-process controls' (IPC). That bit of jargon is defined as "checks that are carried out before the manufacturing process is completed". These are not applied restraints but inspections and procedures which should be performed during the manufacturing process to ensure quality control.

The discussion of 'control' and its definitions, apart from being largely mistaken, is aside the point. IPCs are procedures which must be performed and there's nothing ungrammatical about it.

In this context, exasperated and agitated are not being used as adjectives. They're being used as nouns. Specifically, they are naming conditions or states of being. It would be less idiomatic, but you could rephrase like this: "...between the condition of being exasperated and the condition of being agitated."

This kind of phrase, which uses adjectives like nouns, is fairly common. Here are some examples:

• There's a big difference between well-off and rich.
• Fast is better than slow.
• Happy is the best way to be.

Sometimes nominalization (making a non-noun into a noun) is done by changing the word. In fact, there are related, nominalized forms of exasperated and agitated: exasperation and agitation. This sentence, could have used those forms - i.e. "...the liminal state between exasperation and agitation" - and there are probably style guides that would recommend the use of those nouns, but it's not mandatory.

Here's a useful discussion of the subject on the English Language and Usage site: Is there a term for the use of adjectives as nouns?