To add to Ahmed's fine examples, here you can find some others and, on top of that, an explanation as to the relationship between the perfect participle (having + past participle) and the verb in the main clause:
Perfect participle clauses
Perfect participle clauses show that the action they describe was finished before the action in the main clause. Perfect participles can be structured to make an active or passive meaning.
Having got dressed, he slowly went downstairs.
Having finished their training, they will be fully qualified doctors.
Having been made redundant, she started looking for a new job.
As you can read above, the perfect participle clause expresses an action or a state previous to the action or state in the main clause. In the second example, the main clause is in the future, the idea being that, once they have finished their training, the trainees will become qualified doctors (completing their training is a prior condition to their becoming qualified doctors).
And last but not least, in Table 18-4 Expressing Cause and Effect in Modifying Adverbial Clauses under "Reduction of Adverb Clauses to Modifying Adverbial Phrases" on page 395 of Azar and Hagen's Understanding and Using English Grammar, we can find, among many other examples, this interesting pair of sentences in which the main clause appears in the present or in the past tense depending on how the time frame expressed by the perfect participle is understood:
(e) Having seen that movie before, I don't want to go again.
(f) Having seen that movie before, I didn't want to go again.
The authors explain:
Having + past participle gives the meaning not only of "because" but also of "before."
As you can see, there are no restrictions as to the tense of the verb in the main clause. In fact, (e) can be paraphrased as follows: As I have seen that movie before, I don't want to go again, while (f) can be paraphrased as follows: As I had seen that movie before, I didn't want to go again.
The grammar references we have cited should hopefully satisfy your students.