ABSTRACT
With these notions and notations at our disposal, let us return to the commutativity issue raised in the introduction, and consider commutativity properties of exptF and expsG corresponding to vector fields F and G. This question may be further motivated through the following control theoretic context:
Consider a control system dx
dt = u(t)F(x(t))+ (1− u(t))G(x(t))
with switching control u which can only take values 0 or 1 (on-off controls). During any time interval that the control is turned on the system follows F and during the time intervals that the control is switched off the system follows G.
