Department of Automatic Control
Lund Institute of Technology
The scalar function has a physical interpretation as the stationary density of a substance that is generated in all points of the state space and flows along the system trajectories. If the stationary density is bounded everywhere except at a singularity in the origin, then almost all trajectories tend towards the origin.
The weaker notion of stability allows for applications also in situations where Lyapunov's theorem can not be used. Moreover, the use of density functions has advantages in control theory, for the synthesis of stabilizing controllers. These issues will be addressed in the seminar and the relation between density functions and Lyapunov functions will be further explained.