Unilateral Stabilization at First Approximation

This paper concerns the behaviour of trajectories of a nonlinear control system in the vicinity of a stationary point. The control corresponding to the equilibrium position may belong to the boundary of the set of admissible controls. A linear control system is considered as a first approximation for the original problem. The right-hand side of the linear system generates a set-valued map of a special type known as a convex process. This set-valued map has a number of properties similar to those of a linear operator. They allow us to describe a convex cone which is the region of attraction for the first approximation. It is established that the original nonlinear system has a region of attraction such that the tangent cone to it at the equilibrium position coincides with the region of attraction for the first approximation.