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Journal of Convex Analysis 15 (2008), No. 4, 819--830
Copyright Heldermann Verlag 2008

On Generalized Differentials, Viability and Invariance of Differential Inclusions

Zbigniew Bartosiewicz
Technical University, ul. Wiejska 45a, 15-351 Bialystok, Poland

Ewa Girejko
Technical University, ul. Wiejska 45a, 15-351 Bialystok, Poland

Forward viability and invariance of time-dependent differential inclusions are studied with the aid of generalized differentials. Contingent derivative is compared with a newer concept of generalized differential quotient. It is shown that the latter is more suitable for expressing criteria of viability and invariance, as it better describes the directions tangent to invariant trajectories of differential inclusions. The concept of generalized differential quotient is related to Cellina continuously approximable set-valued functions whose properties are used.

Keywords: Differential inclusion, viability, invariance, Cellina continuously approximable multifunction, contingent derivative, generalized differential quotient.

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