where Ir = RIref
Vin
. Now by putting (5) into (3), the closed
loop nonlinear map describing the two-cell buck converter is
obtained. Note that the closed loop model is nonlinear due to
the presence of quadratic forms such as i2
n, v2
n or in vn. It is
linear only when both d1 and d2 are saturated. Note also that
due to the presence of the saturation function, the closed loop
model is piecewise smooth.