Geodesic
Invariant and Stably Invariant Sets for Differential Inclusions
Informatics and Automation, 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. 
@article{TRSPY_2008_262_a15,
     author = {E. A. Panasenko and E. L. Tonkov},
     title = {Invariant and {Stably} {Invariant} {Sets} for {Differential} {Inclusions}},
     journal = {Informatics and Automation},
     pages = {202--221},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a15/}
}
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E. A. Panasenko; E. L. Tonkov. Invariant and Stably Invariant Sets for Differential Inclusions. Informatics and Automation, Optimal control, Tome 262 (2008), pp. 202-221. http://geodesic.mathdoc.fr/item/TRSPY_2008_262_a15/