Sure, you would close any open tabs before opening the current tab. For identification, you can add a class “open” when a tab is opened. You could also test for css display properties with an if statement.
Something like this should work:
//toggle any open tabs shut and remove the 'open' class
$('.dropdown-container.open').slideToggle(100).removeClass('open');
//add an open class when opening a tab
$('ul li button').click( function(){
$(this).parent().find('.dropdown-container').addClass('open').slideToggle(100);
});