This idea is a really indirect way to go about it, but here's a "Matriarchy" concept centered around chivalry and knighthood.

In this society, "Chivalry" is highly valued as the most important quality a male should have. Being chivalrous implies far more respect to women here than in real life history: A truly chivalrous man will greet a woman like royalty, fufill every request he can, and never so much a dream as hitting, interrupting, or contradicting a woman.

A male acting outside of these expectations isn't necessarily illegal, but such men will remain poor and downtrodden. If a guy wants to climb up to a decent place in society, achieving the rank of a "Knight" is his best bet.

Becoming a Knight awards men with far better housing, employment, and entertainment opportunities than otherwise. It requires years of schooling and trials to ensure the principals of proper male etiquette are dully instilled. Then he needs to find a woman to agree to knight him. This woman becomes his "Princess." He is to show full devotion to her. All of his assets belong to her, and she can veto any of his decisions.

Knights who fail to live up to the code are stripped of their rank and thrown into slavery. The Princess they served can still keep all his assests. She's free to remain a Knightless Lady, but there's nothing stopping her from Knighting another man either.

Poor women who are never able to bond with a worthy aspiring Knight DO exist. But chivalrous teachings and fellow women effectively running society really put them in a higher class than poor men.