Non-citizens being allowed to vote

Under what law are non-citizens being allowed to vote? Ironically, state laws govern voting so states that allow non-citizens to vote may end up imposing on the rest of us, someone, who if only citizens had voted,might not have been elected. It seems logical that the rules for Presidential voting should be the same from state to state. For all other elections state rules could and should apply. I don't want my vote cancelled by a non-citizen, do you? There is no sensible or ethical reason for the United States of America to be lead by someone elected by non-citizens. It makes a joke out of our elections, discourages participation and alters results. And as far as I can see leaves actually citizens with but one right: The right to pay taxes and support the same system that gives illegals all the rest of our rights. Mrs. Carolyn M. Brown