Thanks Jpfeifer for the reply.
In this pdf file on this forum question (State space representation in Dynare), it says that the state vector (in the state-space form) contains all the variables in the model (defined under var). So I think it is talking about y i k a c. But this is wrong, right? The state vector (in the state-space form) contains just the true state/pre-determined variables (k(-1) and a). Assuming we have data on just two control variables (y and c). Then the x in the observation equation is vector of y and c. Now variable i is an unobservable control variable, right? And I guess it is implicit in the state-space representation, most likely associated the state equation. Or we cannot actually say which of the two state-space equations implicitly captures variable i. Or we should just ignore unobservable control variables in state-space representation. But actually it is there, right?