CONICET | Buscador de Institutos y Recursos Humanos

The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems.Several approaches have been reported for the characterisationof these sets, including constructive methods for their computationand procedures to obtain different approximations.However, there are shortcomings in those concepts, in the sensethat no general probability distributions can be considered for thedisturbances affecting the system (which, for example, precludesthe assumption of Gaussian distributions insofar as they are not bounded).Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets,which extend the notions of invariant sets and ultimatebounds to consider `containment in probability´, and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered.We introduce some key definitions for these sets, establish theirmain properties and develop methods for their computation. A numerical example illustrates the main ideas.