As in the discrete-time case, controllability and observability of a continuous-time LTI system may be investigated by diagonalizing the system matrix A. A system with state space representation v(t) = Av(t) + bx(y) y (t) = cv(t) where A is a diagonal matrix, is controllable if the vector b has no zero elements and is observable if the vector c has no zero elements. Consider the continuous-time system.
(a) Find a new state space representation of the system by diagonalizing the system matrix A.
(b) Is the system controllable?
(c) Is the system observable?