dummy variable in state space model

[EViews Glenn]

Yes.

[EViews Glenn]

From the manual...(p. 388-390)

"Each state equation must be linear in the one-period lag of the states."

"State equations may contain exogenous variables and unknown coefficients and me nonlinear in these elements."

"Signal equations must be linear in the contemporaneous states."

So yes, you should be able to do both...

[EViews Glenn]

As with other nonlinear estimation in EViews, the state space routines take starting values from the workfile. There is no guarantee of global concavity to the likelihood functions so that optimal solutions will be starting value dependent. Moreover, it is quite possible (and as you've noted, it often happens) that you will get singularities when starting from different starting values.

[EViews Glenn]

Neither of your state variables has a coefficient on it so I'm not certain how interacting with a dummy variable affects anything (unless all you want to knock out a state for part of the sample). In any event, all you need to do is to multiply the state by the dummy in the signal equation.