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 R(n) 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.