Name that plant

We have a mystery plant. It's an heirloom plant, meaning it multiplies profusely and people pass it along to their family and friends. My mother-in-law gave a clump to me years ago. She got it from her mother in law. From that one clump, we have enough to line our fence, and give to friends and family. It's perennial. Dies every year, comes back every spring and grows to this mammoth size each summer.

The stalk has joints similar to bamboo, but I've looked at pictures of many, many, many bamboo varieties and none are similar.

It starts to bloom every August. That always makes me so sad. It's telling me summer's almost over. The blooming continues here through September and with cooler nights and frost starts to die back.

The blooms are good for pressing and make a nice background in pressed flower pictures. I haven't done that in a long time. I should do that in the morning.

I've looked in every flower encyclopedia I can find, especially southern plants and have never found anything similar. If you have any idea what this is, please let me know. Maybe it is a type of bamboo, since it's invasive, but it's far from being as invasive as bamboo. This is much easier to keep under control. And the stalks never get hard.