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Biological lifelong pair bonding (monogamy). This is rare, but does happen.

At least one reason males seek dominance in a society is to increase their access to mates, and thus have more children then other males, thus their genes are increased in the next generation.

Due to sexual differences between genders, only males tend to do this; specifically in humans a female can only give birth to perhaps twenty children in a "sexual career", but a male can father thousands of children in his sexual career. Therefore, there is an evolutionary upside for males to mate with as many women as possible, but there is no evolutionary advantage for women to do so.

Due to this dimorphism leading to competing mating strategies for spreading one's genes, men (and males in most wild animals) exhibit aggression and dominance over other males, to prevent them from mating and secure more mates for the "alpha". By the same token, in humans with a culture, it serves men to dominate both men and women to ensure their own ready access to reproductive opportunity.

This is true whether the result is the actual production of many children or not; the instinct to take control and subjugate others (by brute force or intelligent strategy) is still there, and stronger in males than in females.

An antidote for that, as a trait, would be lifetime pair bonding, eliminating the need for men to compete for women. Excerpts from the link:

The few animals that do stick together are providing scientists with valuable clues about the biological basis of fidelity. One of the most studied animals in this regard is the mouse-like prairie vole. A male vole will prefer to mate exclusively with the first female he loses his virginity to. And his faithfulness approaches a kind of fanaticism: Far from trying to woo other females, a mated male vole will actually attack them.

In recent years, scientists have traced these unusual behaviors to levels of certain neurotransmitters in the rodents' brains. Interestingly, one of these, dopamine, is also implicated in drug addiction in humans.

That's a plausible explanation for your species too: The female chooses a virgin male, and (biochemically speaking) the male becomes love-addicted to the female for life, he doesn't want to mate with any other female, and the only way for him to get his sex-fix is to please her, which he wants to do. He's literally not capable of being attracted to or aroused by another female.

In a way, you extend the "fallen into crazy love" phase of the relationship indefinitely, for the male. As part of pleasing her (and not suffering from the withdrawal symptoms of being denied sex with her) he lets the woman be in charge and make the decisions.

Presto, Matriarchy.

The Mosuo people of China are descendents of nomad from the Tibetan plateau, a steppe or semi-desert area, so it seems to fit your description.
https://en.m.wikipedia.org/wiki/Mosuo
http://factsanddetails.com/china/cat5/sub87/item182.html#chapter-1

The society is matriarchal though it seems to emanate from some historical and social circumstances. They are basically just the same as their neighboring people, and a Mosuo child raised in a "normative" family would behave the same as the adoptive one. Those traits are cultural and unlikely to be genetic.

The second link states that men were herding the cattle and livestock. Put that in your desert or semi-arid setting of your people. The man travels long distances in search of pasture, and the woman stays at home, tending her children and managing her household. That makes the mother a more dominant figure in the house. As the father is absent next of kins take care of the household.

Postulating a cognitive aspect to sexual dimorphism, where the females are the brains of the clan/tribe/species. Couple this with males being subject to musth, like elephants - where their sex hormonal drives are so strong they cannot be entrusted to leadership. Highly intelligent matriarchal societies would have more subtle ways of co-opting the males into cooperation, including withholding sex, ritual restraints, cultural taboos.

Postulating a reproductive bias toward females which tends to keep males in the minority within populations.

Postulating the female controls paternity, as a means of modulating male behavior, enhancing female control at the most basic level.

Postulating females as the larger of the sexes (as in hyenas). Less plausible.

I don't know about fictional alien humanoids; and I don't know about "environmental factors" which may favor matriarchy; actually, if those humanoids are anything like humans, I'm pretty much convinced environmental factors will matter very little if at all.

But what I do know is that the status of women varies greatly among human societies, both past and present. So I will not speak about fictional alien humanoids, but about real human societies.

What is a "matriarchal" society? Do the English count? After all, their monarch is a woman, and their prime minister is a woman too. But, alas, the English do not live in a desert, quite the contrary; they notoriously live in a green and pleasant land, or so thay say.

As luck would have it, we actually do have here on Earth a relatively well-known example of desert nomads who live in a matriarchal, or at least in a very non-stereotypically-patriarchal, society:

The Tuaregs

• The Tuareg people (/ˈtwɑːrɛɡ/; also spelt Twareg or Touareg; endonym: Kel Tamasheq, Kel Tagelmust) are a large Berber ethnic confederation. They principally inhabit the Sahara in a vast area stretching from far southwestern Libya to southern Algeria, Niger, Mali and Burkina Faso. Traditionally nomadic pastoralists, small groups of Tuareg are also found in northern Nigeria. (Wikipedia, s.v. Tuareg people)




• There are some 3 million of them, which, for a nomadic desert ethnic group is quite a lot.




• Tuareg culture is largely matrilineal. Tuareg women have high status compared with their Arab counterparts. (Wikipedia, ibid.)




• In Tuareg society women do not traditionally wear the veil, whereas men do. (Wikipedia, ibid.)

On the left, a Tuareg woman; photograph by Alain Elorza, available on Wikimedia under the CC BY-SA 2.0 license. On the right, a Touareg husband (with a full-face veil) and wife (with no veil); photograph by MataHali available on Wikimedia under the CC BY-SA 4.0 license.

• 
  Tuareg social status is transmitted through women, with residence often matrilocal. Most women could read and write, while most men were illiterate, concerning themselves mainly with herding livestock and other male activities. The livestock and other movable property were owned by the women, whereas personal property is owned and inherited regardless of gender. (Wikipedia, s.v. Matrilineality)

Bonuses: they have an actual noble class; they keep slaves, modern sensibilities be damned; they have a very good-looking flag; they speak Berber languages, written (sometimes) with a deliciously exotic alphabet.

To be as realistic as we can, we can look at the closest non-extinct relatives to homo sapiens we have on our planet. Our closet relatives (as we believe today), are 4 species, in 2 categories:

1. Gorillas (2 species: eastern and western )


2. Pans (2 species: Chimpanzees and Bonobos )

Unfortunately for your story, none of these have a natural habitats in the desert, but they are as human like as we can possibly get, while still having real data to look at.

As it happens, these 4 species have variations in gender roles. One of them in particular does have (quite famously) a very strong matriarchal aspect: bonobos

It therefore becomes interesting to investigate bonobos closely, and see what other traits they have. Establishing causality is not straightforward of course, but this has not stopped people from using bonobos to argue for their favorite trait as the cause for matriarchal structure.

On the topic of sexuality, bonobos second most famous trait, is their sexual frivolity and absence of long term bonding. Bonobos are, according to Christopher Ryans book, "sex at dawn", the only other species observed to indulge in large scale recreational sex.

Perhaps there is some credence to the logic that if there are no long-term relationships, there are no need for males in patriarchal societies to defend their women and thus adept to less dominant behavior. Also, if there is no sexual frustration in the male population, the male violent tendencies may be decreased, and females can form the kind of "committee leaderships" found in Bonobo social structure.

I do not believe that is anywhere near the full story for humans. Nonetheless, for your story, having a plausible humanoid species on another planet be more matriarchical, I believe it could be a good idea to make them more Bonobo-like.

EDIT: I did mention that the Musou people are referenced in the book by Ryan, but quickly removed it. I have heard some find it offensive.

Many societies that appear to patriachal in fact aren't.

For example, among European farmers, there was a strict division of labor and power. The man ruled over the work on the farm and the farmhands, the woman ruled over the house, the children, and the scullery maids. Basically, what you had were two areas of government that were largely independent of each other. And who prevailed in things that had to do with the whole farm depended on the personality of the man and woman and their arrangement.

Similar differenced could be found among the Native Americans. While the male warriors appeared to be dominant to outsiders, because they were the ones who talked to them and made decisions of war, in some tribes the women (or a converence of men and women) ruled the tribe in peace.

So maybe you can differentiate the roles of men and women a bit, give each different areas over which they rule. Patriarchy (and matriarchy) seldom are the absolutes that they are made out to be.