On the global linearization of bilinear systems

The problem of finding a global state space transformation to transform a given single-input homogeneous bilinear system to a controllable linear system on Rⁿ is considered here. We show that the existence of a solution of the above problem is equivalent to the existence of a local state space transformation that carries the corresponding bilinear system locally to a controllable linear one. The complete analysis of the globally state linearizable bilinear systems in R² and R³ is also included.