  We present a sufficient condition for the stability property of extremal
graph problems that can be solved via Zykov's symmetrisation. Our criterion is
stated in terms of an analytic limit version of the problem. We show that, for
example, it applies to the inducibility problem for an arbitrary complete
bipartite graph $B$, which asks for the maximum number of induced copies of $B$
in an $n$-vertex graph, and to the inducibility problem for $K_{2,1,1,1}$ and
$K_{3,1,1}$, the only complete partite graphs on at most five vertices for
which the problem was previously open.
