Attractors and partial stability of nonlinear dynamical systems.
The paper presents a study of two (very similar, but not, in general, identical) concepts: the first is a concept of attracting invariant sets (submanifolds), the other is a concept of partially asymptotic stable systems. The paper establishes relations between their local properties and enables to unify the methodologies of their analysis. By using recent results of the stability theory and techniques of the geometric theory of control, Lyapunov-like sufficient conditions of partial stability and set attractivity are proposed. Simplified solutions for the problems of set attractivity and partial stability are obtained.
scientific article; zbMATH DE number 2056277