LaSalle's invariance principle

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. == Global version == Suppose a system is represented as x ˙ = f ( x ) {\displaystyle {\dot {\mathbf {x} }}=f\left(\mathbf {x} \right)} where x {\displaystyle \mathbf {x} } is the vector of variables, with f ( 0 ) = 0 .

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