French Past Imperative ~ Impératif passé

The past imperative is a compound verb. It is formed with the imperative form of the auxiliary verb (either avoir or être) plus the past participle of the main verb.

The French past imperative is very rare, because its usage is restricted to a single situation: it gives a command for something that must be done before a certain time. 

In the first example, "Have this report written by tomorrow," when tomorrow comes the report will already be written, so the writing of it will be in the past, ergo, the past imperative. If you use the regular imperative, "Écris ce rapport demain," the report won't yet be written when tomorrow rolls around: you will be writing it tomorrow. On the other hand, you could just say "Écris ce rapport avant demain" and avoid the past imperative altogether - probably another reason that it is so rare.

The past imperative is kind of similar in nuance to the past infinitive, except that it indicates a command rather than a statement of fact.

Because the past imperative is so rare, there's really no need to learn how to use it, but you should be able to recognize it.