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A.L. Dontchev, M. Krastanov, V.M. Veliov:
"w-limit sets for differential inclusions";
in: "Analysis and Geometry in Control Theory and its Applications", Springer, 11, 2015, ISBN: 978-3-319-06916-6, S. 159 - 169.

This paper is about locating ω-limit sets for solutions of differential inclusions with not necessarily continuous right side. Based on the LaSalle principle we assume that as time t→∞ the set of solutions approaches a closed subset S of Rn and then consider the dynamics restricted on S to find the location of the ω-limit set by utilizing nonsmooth Lyapunov type functions over a neighborhood of S; then we prove that this location is also valid for the original dynamics. We apply our result for nonsmooth differential equations and compare it with some recent works.

http://dx.doi.org/10.1007/978-3-319-06917-3_6