How do I initialize the state of a digital filter in Direct Form II?
The difference equations for this filter are:

y[n] = b0 w[n] + b1 w[n-1] + b2 w[n-2]
w[n] =    x[n] - a1 w[n-1] - a2 w[n-2]


To achieve steady-state, w[n] == w[n-1] == w[n-2]. Call this value w. Solving the second difference equation, we find w = x/(1 + a1 + a2), where x is the steady-state input value.