If one made a bracha (for example an woman by tevillah) "Baruch Atah HaShem Elokeinu Melech HaOlam al ha-tevillah" (and forgot to say "asher kidashanu b'mitzvosav vitzaivanu…") are they yotzee bedieved? (Have they fulfilled their obligation of reciting the bracha.)
Although I haven't found anything concrete in this I saw in Kovitz Beis Aharon V'Yisrael a short piece that raises this point.
There are 2 cases brought there. One if the person left out the word "vitzavanu" and another if they left out everything, "asher kidashanu b'mitzvosav vitzaivanu"...
In the first case he wants to say you are yotzee since you said "asher kidashanu b'mitzvosav" it's understood your intention when you end off the bracha with whatever mitzvah you are doing (in his case, "lhadlik ner shel channukah".) However if the person left out everything about the idea of "mitzvas" then he says that you wouldn't be yotzee.
(Note: While I don't feel this is a complete answer it's at least one person who I found that speaks about it. I will improve the answer if more is found.)
The halakhah (Rambam, Hil. Berakhot 1:6) is that "[A person who] changes that text fulfills his obligation nonetheless - since he mentioned God's name, His sovereignty, and the subject of the blessing." The crucial aspect here is "the subject of the blessing" (inyan ha-berakha). According to R. Avraham ben ha-Rambam (Sefer ha-Maspik le-Ovdei Hashem, ed. N. Dana, p. 237), the words "asher kiddeshanu be-mitzvotav" parallel the conclusion of birkot ha-nehenin ("Blessed...the one who created this"). In other words, asher kiddeshanu is the primary purpose of the berakha--to praise God for having sanctified us with his commandments. Thus, if someone left out these words, it would seem that he is lacking the "inyan ha-berakha," and he would not be yotzei.
See Rambam Hilchos Berochos 1:6 and in the Kesef Mishne there. Also Rashba on Berochos 40b s.v. Veha Be'inan. For the bottom line see Shulchan Aruch 167:10 and Shulchan Aruch HoRav 167:13 (especially where he says ואפילו לא הזכיר שם הפת כלל שאמר מריה דהאי) and in Seder Birkas Hanehenin 13:4. it will come out that since the person said Shem Umalchus and (only) the concept of the Beracha it would be valid.