The author consider a general (i.e. not necessary continuous) impulsive semidynamical system. He proves in this context, two classical LaSalle’results, namely the Invariance Principle and the Asymptotic Stability Theorem. In particular, he generalizes a result of S. K. Kaul
[J. Appl. Math. Stochastic Anal. 7, No. 4, 509–523 (1994; Zbl 0857.54039
)]. Moreover, some applications are given, in particular for impulsive semidynamical systems on the plane.