This paper deals with notions which allow us to compare the degree of developments of dynamic systems. The classical definition of stability can be obtained by comparing the considered system with the trivial equation Ẋ ¦ 0. In the linear cases, this definition leads to the comparison of the top essup - exponents of these systems. We are also concerned with the control problem of Lyapunov exponents for choosing “a stablest system”. The existence of optimal controls is proved