Generally speaking, women are exempt from time bound positive Mitzvot - מצות עשה שהזמן גרמא. Lulav and Sukkah are examples of Mitzvot that women are not commanded to fulfill. If, however, women wish to perform these mitzvot, they are permitted to do so. (The custom, however, is for women not to wear Tallit and Tefillin) (רמ"א אורח חיים יז:ב, לח:ג). The question is whether women are permitted to recite a Beracha over these mitzvot. Generally, Ashkenazic women recite Berachot on these Mitzvot whereas Sephardic women usually do not. We will explore the sources of these divergent customs from the Gemara to contemporary sources.
The Gemara in Rosh Hashana (דף לג.) records a difference of opinion among the Tannaim whether women may perform a Mitzvah from which they are exempt. Tosafot (שם ד"ה ר' יהודה) demonstrates that the Halachah follows the opinion of Rabbi Yosi and Rabbi Shimon who rule that it is permissible. They cite the Gemara in Chagiga (דף טז:) which records that women were permitted to place their hands on the head of the animals they brought as sacrifices (סמיכה) in order to provide women with spiritual satisfaction - כדי לתת נחת רוח לנשים. They also cite the Gemara in Eruvin דף צו:() which records that King Saul's daughter wore Tefillin, and the prophet Yonah's wife made a pilgrimage three times yearly to the Bet HaMikdash. The Rambam also rules that women are permitted to perform Mitzvot from which they are exempt (הל' ציצית ג:ט).
The question is, however, whether women may recite a Bracha when performing Mitzvot they are exempt from. Rambam (שם) and other Rishonim, Rashi cited by the Or Zarua )ב:רסו(, the Hagahot Maimoniot (הל' מ) on the aforementioned Rambam, and the Maggid Mishnah all rule that women may not utter a blessing. One of the reasons for this ruling is articulated by the Smag (מצות עשה מב) who says that since women are exempt from performing the Mitzvot, they cannot recite a Bracha which states וצונו, that Hashem has commanded us to perform this Mitzvah.
On the other hand, the previously mentioned Tosafot cites the celebrated opinion of Rabbeinu Tam that women are permitted to make a Brachah on a מצוה עשה שהזמן גרמא. Indeed, many Rishonim share his view (Ramban, Ritvah, and the Ran commenting on Kiddushin לא.). These Rishonim cite various proofs to this ruling, including the celebrated statement in Kiddushin לא.() that גדול המצווה ועושה ממי שאינו מצווה ועושה - "That those who do and are commanded to are rewarded more than those who do but are not commanded." However we see that mitzvot performed by those not commanded still have halachic significance, and hence reciting a blessing would be permitted.
The Ran, commenting on Kiddushin לא. (ד"ה צאו) writes that "it is appropriate for women to say וצונו since men are commanded and women have a relationship to these mitzvot, as we see that they receive a reward for performing them." The Ritva adds a reason why women may say וצונו, "because they (women) are part of the Jewish people who are commanded to perform these mitzvot." Tosafot explain that women reciting a bracha on מצות עשה שהזמן גרמא are not reciting the Bracha as a wasted blessing (ברכה שאינה צריכה) and are not in violation of taking God's name in vain. They say that because the prohibition of saying an unnecessary bracha is Rabbinic in nature, and hence the Rabbis of the Gemara are empowered to rule that someone may recite a blessing on a Mitzvah they are not required to do. The Rambam, on the other hand, appears to be of the opinion that the prohibition to recite an unnecessary bracha is מדאורייתא in nature (see Rambam's responsa no. 48 in the Blau edition).
Practically speaking, there exists a difference of opinion. Rav Yosef Karo, in the Shulchan Aruch (אורח חיים יז:ב, תקפט:ו) rules in accordance with the view of the Rambam, that women may not recite a blessing on a מצות עשה שהזמן גרמא. The Rama, however, notes that the practice of Ashkenazic women is to follow Rabbeinu Tam's ruling that a bracha may be recited. This continues to be the undisputed practice of Ashkenazic women to this day.
Sephardic women, however, it would seem would follow Rav Yosef Karo's ruling that a bracha should not be recited. Nevertheless, many Sephardic women do recite a bracha on certain מצות עשה שהזמן גרמא. They follow the approach of the great Sephardic authorities, Rabbi Chaim Yosef David Azulai (Chida) and Sdei Chemed כללים מערכת מ' כלל קל"ו() who both encourage even Sephardic women to recite a bracha on some of these mitzvot. Contemporary Sephardic Rabbinic authorities differ regarding this practice. Rabbi Ovadia Yosef, former Sephardic Chief Rabbi of Israel, strongly urges Sephardic women to follow Rav Yosef Karo's ruling not to utter Berachot on מצות עשה שזמן גרמא (יחוה דעת א:סח). Rabbi Chaim David Halevi, Chief Sephardic Rabbi of Tel Aviv, in his work "עשה לך רב" (חלק ב סימן לג) endorses the practice of many Sephardic women to recite Berachot on certain מצות עשה שהזמן גרמא. Rabbi Ezra Basri, a Sephardic Dayan in Jerusalem, told this author that he also believes the practice of these Sephardic women to be correct.
Accordingly, Ashkenazic women recite Berachot on the מצות עשת שהזמן גרמא which they have a custom to perform, such as Sukkah and Lulav. Sephardic women, though, should consult their Rabbi for guidance regarding whether they should say a Beracha on Sukkah and Lulav.