On stability and controllability for semigroup actions. (English) Zbl 1362.37046

Souza, Josiney A.; Tozatti, Hélio V. M.; Rocha, Victor H. L.

Topol. Methods Nonlinear Anal. 48, No. 1, 1-29 (2016).

Summary: This paper deals with stability and controllability for semigroup actions by using the topological method of admissible family of open coverings. The main results state a relationship of stable sets and control sets. The classical notion of controllability relates to the Poisson stability. The concept of prolongational control set relates to the Lyapunov stability.

MSC:

37B55	Topological dynamics of nonautonomous systems
37B05	Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37B25	Stability of topological dynamical systems
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B05	Controllability

Keywords:

semigroup action; stability theory; control theory