In the field of control theory, there has been an increase in interest in studies on the equivalence of robust and optimum control of linear control systems. To provide appropriate constraints for increased stability and control performance, we study in this work the link between linear systems under robust and optimum control as well as the equivalence between the two. We will present in this research significant changes to the way constraints are designed, which may also improve system control and stability. We will show that with theorems and examples.