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LaSalle’s theorems in impulsive semidynamical systems. (English) Zbl 1183.37024
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 {\it 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.

MSC:
37B25Lyapunov functions and stability; attractors, repellers
34A37Differential equations with impulses
54H20Topological dynamics
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Full Text: DOI
References:
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