I understand that the state-space representation of the DSGE model is basically about unobserved (state) variables (x) and observed variables (y), and then some shocks and measurement errors.

Why sometimes ‘y’ is labeled as a vector of control variables (see, Graduate Macro Theory II:

Notes on Using Dynare by Eric Sims) or a subset of control variables (see, A Guide to Specifying Observation Equations for the Estimation of DSGE Models by Johannes Pfeifer)?

My understanding is that some control variables are unobserved, so how is that captured in the state-space representation. Via the state equation or the observation equation??

State equation contains only true states (thus, predetermined variables), or does it also include unobserved controls?? Many thanks!