Stability of a class of differential inclusions

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.