How can I implement a K-Map with negative feedback?
If the present output depends on previous output, then use the previous output as as one of the variable in truth table and K-map.

Take JK flipflop as an example:

-------------------
J  K  Qn    Qn+1
-------------------
0  0   0     0
0  0   1     1
0  1   0     0
0  1   1     0
1  0   0     1
1  0   1     1
1  1   0     1
1  1   1     0
------------------