The only options to remove a perennial weed are to manually remove it, smother it (not very feasible when it's growing amongst desirable plants), or spot-treat it with systemic herbicide. Seedlings germinating as a result of soil disturbance (like from planting annuals each year) can perpetuate the problem unless they are removed while very young, and using mulch over any exposed soil (after you put in the annual transplants, or after any annual seedlings have matured enough not to be smothered by mulch) can discourage future germination.

Manual removal for perennials can work, but may take multiple seasons, as can systemic herbicide treatments if the plant regrows easily or isn't as vulnerable to the chemical. The active ingredient glyphosate is a commonly-used systemic option, but there are others. Make sure any spray used does not contact desirable plants, or it could damage or kill them.

Sometimes cutting the perennial weed back and waiting for a bit of regrowth before spraying it is an easier approach, since that will require less herbicide (and is easier to limit the exposure to other plants) than treating a larger weed with more foliage and a greater height/spread. Over time, manual removal weakens the plant by forcing it to keep using-up root energy stores to make the new growth, and if it's cut down again before that new growth can photosynthesize enough to replenish those root reserves, eventually the plant runs out of energy and dies. A combination approach -- repeated manual removal, then an herbicide treatment -- may also work well. Often, perennial weeds respond best to systemic herbicide treatment in the latter half of summer or just before autumn, when the plant is sending carbohydrates and other materials from the leaves into the roots for winter storage before the top growth dies back. The absorbed chemical then "hitches a ride" more efficiently into roots compared to spring or early summer treatments.

Miri