A class of $\mu$-commutative bilinear control systems

A class of $\mu$-commutative bilinear control systems is defined and the properties of coefficients of a $\mu$-commutative system are studied. A $\mu$-commutative scalar control system is studied and an explicit representation for its input-output mapping is derived. This mapping is used to study the properties of a system, particularly the geometry of its reachable set.