Many systems encountered in science and engineering -- such as biological populations, chemical reaction networks, energy storage devices, traffic flows, and thermodynamic processes -- share a fundamental feature: their states and control inputs are inherently nonnegative. These positive systems obey dynamics that differ significantly from those typically studied in classical control theory.

In this talk, we explore how positivity reshapes the foundations of stability and control design. Standard notions based on symmetric norms and classical Lyapunov conditions give way to asymmetric metrics and fundamentally different stability principles. In particular, the familiar Control Lyapunov Function (CLF) framework must be reinterpreted, leading to new and less restrictive conditions that enable elegant and powerful design methods.

Building on these ideas, we present general and systematic recipes for both stabilization and inverse optimal control of systems with positive states and controls. Rather than being a limitation, positivity opens the door to a rich and structured theory with strong practical relevance.

To illustrate these concepts, we will use predator-prey dynamics as an intuitive and visually compelling example, highlighting how complex interactions can be guided toward stable and desirable behaviors.

Registration link (Free but compulsory):

https://www.laas.fr/fr/formulaires/seminaire-fellow-amabassadeur/