Realizing practical quantifier elimination (QE) has been developed by several researches, since cylindrical algebraic decomposition, as a great breakthrough, was invented by George Collins in 1973. Now it becomes a powerful computational tool for solving real problems described by algebraic inequality constraints. In this talk, in order to show its ability, we will focus on the recent developments on its application to control theory and will explain how we can compute the exact solution and parametric optimization efficiently with help of effective equality constrain solving by Groebner basis. Moreover, we will explain recent practical improvements on algorithms of QE.