Consider the first-order plant described by

and a prediction observer described by (9-38).

(a) Construct a single set of state equations for the plant-observer system, with the state vector $\left[x\right(k\left)q\right(k{)}^T]$ and the input $u\left(k\right)$ (i.e., there is no feedback).

(b) Show that this system is always uncontrollable, regardless of the value of observer gain $G$.

Transcribed Image Text:

x(k + 1) = Px(k) + Qu(k) y(k) = Rx(k)