There is a Mitzvah of prolonging Shabbat beyond its official end time known as Tosefet Shabbat (lit. an addition to Shabbat). By lengthening Shabbat we demonstrate that it is dear to us and are not in a hurry to escort it out, as it were. The Shulhan Aruch (O.H. 293:1) writes that Arvit should be delayed on Motzaei Shabbat so that Shabbat extends beyond its normal end time. The Mishna Berura (ibid:1), quoting the Bach, explains that one way to lengthen Shabbat is to recite different Mizmorim, such as Mizmor 67, before Arvit. Indeed, the Moroccan custom is to sing several Mizmorim, including Michtam LeDavid (Mizmor 16), which is sung in a slow melody.
Many Siddurim also include Mizmor 119 (also known as Alpha Beta because it follows the order of the Hebrew alphabet) as well as all the Shir Hama’alot (Mizmorim 120-134) before Arvit of Motzaei Shabbat. However, the Kaf HaHaim (ibid:205), quoting the Sha’ar Hakavanot, writes that the Arizal refrained from reading all these Mizmorim. As well, the Ben Ish Hai (Mekabtziel, Parashat Haye Sarah, § 32) that the original custom in his locale was to recite the Alpha Beta, but upon learning the Arizal’s approach, they discontinued it. Nevertheless, the Ben Ish Hai explains, Mizmor 66 should be recited since it is auspicious for one’s livelihood.
The Moroccan custom (with some variation) is to recite Mizmor 15 (Hashem Mi Yagur BeAholecha), Mizmor 16 (Michtam LeDavid), Mizmor 144 (LeDavid Baruch A-donai Tzuri), Mizmor 67 (Lamnatzeah Binginot) and Mizmor 24 (LeDavid Mizmor LA-donai Haaretz Umloa). Traditionally, the last Mizmor is recited with one’s hands open since it too is auspicious for receiving Hashem’s abundance. Rabbi Issachar Eilenbog (Beer Sheva Siman 74) questions why opening one’s arms is not considered imitating the praying practices of the idol worshippers and thus writes it is forbidden to pray with open hands. However, Rabbi David Cohen-Scali (Kiryat Hana David Siman 13) addresses this question and explains that praying for one’s livelihood is done with open hands to receive Hashem’s abundance and not in a way of idol worshippers.
Interestingly, Rabbi Israel Moshe Hazan (Kerach Shel Romi, § 1, pg. 4) writes that the only extant Mizmor as chanted by David HaMelech is Mizmor 144, which is what he would sing when going out to war. The proof of this, he writes, is that he visited many communities and they all chanted this Mizmor in the same tune, more or less.
Summary: There is a Mitzvah to prolong Shabbat and this is accomplished by chanting a series of Mizmorim.