Title: Robust Stability and Feedback Stabilization for Systems with a Continuum of Equilibria
Abstract: For a dynamical system with a continuum of equilibria, arising for example in the analysis of consensus, the usual concept of asymptotic stability may not be appropriate. For a discrete-time dynamical system with nonlinear and multivalued dynamics, the talk discusses a more applicable stability property, sometimes referred to as semistability. Necessary and sufficient Lyapunov-like conditions for the property are presented, along with results on its robustness. Then a control system is studied, in which the stability property can be achieved through open-loop controls. Two stabilizing feedback constructions are presented. Robustness of the stabilizing feedback and related control Lyapunov functions are discussed
Biography: Rafal Goebel received his Ph.D. in mathematics in 2000 from the University of Washington. He held postdoctoral positions at the Departments of Mathematics at University of British Columbia and Simon Fraser University in Vancouver, and at the Electrical and Computer Engineering Department of University of California, Santa Barbara. In 2008, he joined the Department of Mathematics and Statistics at Loyola University Chicago. He received the 2009 SIAM Control and Systems Theory Prize and is a co-author of the Hybrid Dynamical Systems: Modeling, Stability, and Robustness book. His interests include convex, nonsmooth, and set-valued analysis; control, including optimal control; hybrid dynamical systems; mountains; and optimization.