Differential Geometric Conditions for Koopman Linearizability of Control-Affine Systems
When can curved control systems be transformed into straight-line ones?
Researchers identified mathematical conditions that determine whether a nonlinear control system can be converted into a simpler linear form using a technique called Koopman linearization. The conditions—based on the geometric properties of the system's equations—are both necessary and sufficient for this transformation to work, providing engineers with a practical checklist to assess whether linearization is possible before attempting it.
Control engineers routinely work with nonlinear systems (robots, aircraft, power grids) that are hard to analyze and control. If a system can be Koopman linearized, standard linear control techniques become available, making design faster and more reliable. These geometric conditions let engineers quickly determine whether linearization will work for their specific system, avoiding wasted effort on impossible transformations.