LaSalle's invariance principle (also known as the invariance principle, Barbashin-Krasovskii-LaSalle principle, or Krasovskii-LaSalle principle ) is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system. LaSalle's invariance principle (also known as the invariance principle, Barbashin-Krasovskii-LaSalle principle, or Krasovskii-LaSalle principle ) is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system.