會議室：騰訊會議室ID938 648 662
Convergence in uncertain linear systems
State convergence is essential in several scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, monotone game theory, multi-agent learning over time-varying networks. We study the state convergence in both continuous- and discrete-time linear systems affected by polytopic uncertainty, where we complement the canonical definition of (weak) convergence with a stronger notion of convergence, which requires the existence of a common kernel among the generator matrices of the difference/differential inclusion (strong convergence). We investigate under which conditions the two definitions are equivalent, characterizing convergence by means of LaSalle and Lyapunov arguments and separability of the eigenvalues of the generator matrices. Finally, we show that, unlike asymptotic stability, state convergence lacks of duality.
Filippo Fabiani is currently a post-doctoral Research Assistant in the Control Group at the Department of Engineering Science, University of Oxford, United Kingdom. He received the B.Sc. degree in Bio-Engineering, the M.Sc. degree in Automatic Control Engineering, and the Ph.D. degree (cum laude) in Automatic Control, all from the University of Pisa, in 2012, 2015, and 2019 respectively. In 2017-2018, he visited the Delft Center for Systems and Control at TU Delft, where in 2018-2019 he was post-doctoral Research Fellow. His research interests include game theory, optimization and control of complex uncertain systems, with applications in generation and load side control for power networks and automated driving.