# Output feedback stabilization of non-uniformly observable control systems

Thursday 14th September 2020, 2pm – 3pm.

Lucas Brivadis, PhD student at LAGEPP, Lyon, France (under the supervision of Ulysse Serres and Jean-Paul Gauthier)

When only part of the state of a control system is known, state stabilizing feedback cannot be directly implemented. One must achieve output feedback stabilization instead. A sufficient condition for a globally) state feedback stabilizable control system to be (semi-globally) output feedback stabilizable is the uniform observability of the system, that is observability for all input. However, it is not generic for control systems to be uniformly observable. Investigating this issue, one can distinguish two cases of study: either the system is not uniformly observable, but the target point corresponds to an input that makes the system observable, either the control is singular at the target point. In the former case, we show how a generic smooth additive perturbation of the state stabilizing feedback allows to get observability along the trajectories of the closed-loop system. Also, if the system is dissipative, no perturbation is needed to achieve dynamic output feedback stabilization. In the latter case, we show on an example how to immerse the original system into a dissipative one, either finite or infinite dimensional. This strategy allows to achieve dynamic output feedback stabilization.

See slides