salle A. Turing CE4
31 October 2013 - 14h00
Set-theory and invariance for complex systems
by Mirko Fiacchini from GIPSA-lab, Grenoble
Abstract: The problem of characterizing the regions of stability and convergence, i.e. the domains of attraction, underlies most of the results in control theory, as stability and convergence are usually essential properties of a control law. Also the Lyapunov theory for stability, for instance, is implicitly concerned with the characterization of the regions of the state space where stability and convergence are assured. The techniques based on set-theory and invariance provide elegant and powerful tools, both from the theoretical and computational point of view, to address such issues. On the other hand, while those methods are well assessed in the linear context, their application becomes nontrivial when more complex systems are dealt with. The objective of my research is to extend and adapt the set-theory and invariance approach to certain complex systems, such as switched, hybrid, interconnected and saturated ones.