1. Exogenous variables: controllability and observability
Consider the metasystem (5.44) with A and B as given by (5.45)
(a) Using the algebraic controllability test (5.23), show that the metasystem is not
controllable. (This result is intuitively obvious.)
(b) Assume that only the state x (and not $x_0$) is measured, i.e., y = Cx, and that the
original system $\dot{x} = Ax + Bu$ is observable (i.e., $[C', A'C',..., (A')^{k-1}C']$ is of rank k).
Discuss the conditions under which the metasystem is observable.