Paper Info
Title
Asymptotic properties of solutions to set dynamical systems
Abstract
Dynamical systems with trajectories given by sequences of sets are studied. For this class of generalized systems, notions of solution, invariance, and omega limit sets are defined. The structural properties of omega limit sets are revealed. In particular, it is shown that for complete and bounded solutions, the omega limit set of a bounded and complete solution is nonempty, compact, and invariant. Lyapunov-like conditions to locate omega limit sets are also derived. Tools from the theory of set convergence are conveniently used to prove the results. The findings are illustrated in several examples and applications, including the computation of reachable sets and forward invariant sets, as well as in propagation of uncertainty.
Year
DOI
Venue
2014
10.1109/CDC.2014.7039736
Decision and Control
Keywords
Field
DocType
Lyapunov methods,set theory,time-varying systems,Lyapunov-like conditions,asymptotic properties,dynamical systems,forward invariant sets,generalized systems,omega limit sets,reachable sets,set convergence theory,set dynamical systems,structural properties
Convergence (routing),Mathematical optimization,Propagation of uncertainty,Invariant (physics),Mathematical analysis,Pure mathematics,Omega,Dynamical systems theory,Invariant (mathematics),Mathematics,Limit set,Bounded function
Conference
ISSN
Citations 
PageRank 
0743-1546
1
0.48
References 
Authors
3
1
Name
Order
Citations
PageRank
Ricardo G. Sanfelice121627.88