Abstract
Stability of differential inclusions \({\dot x}\)∈F(x(t)) is studied by using minorant and majorant mappings F − and F +, F −(x)≤F(x)≤F +(x). Properties of F −,F + are developed in terms of partial orderings, with the condition that F −, F + are either heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, including the case of a single equilibrium point, and are illustrated by examples of control systems.
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Diamond, P., Opoitsev, V. Stability of a Class of Differential Inclusions. Dynamics and Control 11, 229–242 (2001). https://doi.org/10.1023/A:1015271918899
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DOI: https://doi.org/10.1023/A:1015271918899