Help removing invasive tropical grass plant

Can anyone help me with some information on how I can remove a large tropical grass like plant that is invading my entire garden?

A few years back I didn't have much growing in my garden (I am VERY new to gardening) and I noticed some shoots growing on one of my borders. I let them grow and it turned out to be a tropical grass type plant. It flourished to the point where it got to approx a meter and a half high and covered about three metres of my border!
I have cut it back vigerously to just three large root balls - but I haven't a clue how to get rid of these. Is there anything I can apply that will kill them off? I have tried to disect the root ball with a spade prior to digging up - but the spade just bounces off as the root ball is so dense!
Also, worrying, tiny clumps of offshoots have started appearing in other parts of my garden....any suggestions anyone?

Thanks in advance for any help.

Re: Help removing invasive tropical grass plant

Reply from Gardens by Mike Palmer

Hello Francis. Hmmm, doesn't sound good but there'll no doubt be a way of removing this.

Do you have a photo of the "offender" before I offer some advice?

Re: Re: Help removing invasive tropical grass plant

Reply from Francis Callaghan

This is what the root ball looks like after I have cut back the leaves. Also, stalks used to grow with brown seed pods hanging from them.

Re: Re: Re: Help removing invasive tropical grass plant

Reply from Mary Starling

It looks very much like pendulous sedge to me. If you live in a marshy area it will thrive.
It disperses by seed so cutting it back and weeding regularly will rid your garden of it.
If not close to the house you can dig up the root-balls after plenty of rain, autumn is a good time but the seed pods will have done their job so you must weed or use a weedol-type weedkiller regularly through the growing season.
.

Re: Help removing invasive tropical grass plant

Reply from Gardens by Mike Palmer

Hello, yes fully agree with Mary. This plant self seeds like nobody's business, but you will get rid of it. Good luck!