Geodesic
Invariant and Stably Invariant Sets for Differential Inclusions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 202-221.

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We discuss conditions, in terms of Lyapunov functions, under which a given set in the extended phase space of a nonautonomous differential inclusion becomes positively invariant, invariant, stably invariant, or asymptotically stably invariant. We also derive conditions under which the integral funnel of a differential inclusion is recurrent in time. A series of examples are considered. 
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E. A. Panasenko; E. L. Tonkov. Invariant and Stably Invariant Sets for Differential Inclusions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 202-221. http://geodesic.mathdoc.fr/item/TM_2008_262_a15/

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