  We studied experimentally the effect of a stripe-like domain structure in a
ferromagnetic BaFe_{12}O_{19} substrate on the magnetoresistance of a
superconducting Pb microbridge. The system was designed in such a way that the
bridge is oriented perpendicular to the domain walls. It is demonstrated that
depending on the ratio between the amplitude of the nonuniform magnetic field
B_0, induced by the ferromagnet, and the upper critical field H_{c2} of the
superconducting material, the regions of the reverse-domain superconductivity
in the H-T plane can be isolated or can overlap (H is the external magnetic
field, T is temperature). The latter case corresponds to the condition
B_0/H_{c2}<1 and results in the formation of superconductivity above the
magnetic domains of both polarities. We discovered the regime of edge-assisted
reverse-domain superconductivity, corresponding to localized superconductivity
near the edges of the bridge above the compensated magnetic domains. Direct
verification of the formation of inhomogeneous superconducting states and
external-field-controlled switching between normal state and inhomogeneous
superconductivity were obtained by low-temperature scanning laser microscopy.
