Foundations of infinite-dimensional input-to-state stability theory (Mironchenko, Uni Passau)
Time: 05.12.2020, 16:15-17:15 Uhr
Room: 03.323 Besprechungsraum Chair in Applied Analysis (Alexander von Humboldt-Professorship)
Foundations of infinite-dimensional input-to-state stability theory”;
Andrii Mironchenko, Universität Passau
During the last years the input-to-state stability (ISS) theory of infinite-dimensional systems has been developing at a staggering pace. Theoretical tools, developed on the basis of semigroup and admissibility theories, Lyapunov methods, and PDE theory allowed to investigate robust stability and stabilization of linear and nonlinear PDEs of parabolic and hyperbolic type, ODE-PDE and PDE-PDE cascades, both with boundary and distributed disturbances. This makes ISS theory for distributed parameter systems an ideal basis for robust stability analysis and robust control of heterogeneous interconnected systems with boundary and in-domain couplings. In this talk, we give an overview of the state of the art of the infinite-dimensional ISS theory and describe some challenging open problems.