How can we introduce exogenous or predetermined variables in the kalman filter ‘s measuramet equation?

In other words, take the state-space representation of a dynamic system as in Hamilton’s book (1994), equations 13.1.1 and 13.1.2.

The measurament equation is y_t = A’ x_t + H’ csi_t + w_t , where x_t is a vector of exogenous (observable) variables. Is there a way to let dynare know that x_t is an exogenous observable vector?

as a short-cut i introduced an equation x_t = x_t-1 + nu_t (where nu_t is iid). I noticed, however, that the stderr for nu affects the smoothed estimates of csi_t even if the model is pure backward looking. Is it possible?

Thanks!

Beta