$x_{k+1} = 0 \cdot x_k + 0 \cdot u_k$
Terms
| Term | This example | Why |
|---|---|---|
| controllable | ✓ | $x_{k+1} = 0 \cdot x_k + 0 \cdot u_k$ is controllable (to the origin) because every state reaches $0$ after one step, and so it is also stabilizable. |
| stabilizable | ✓ | |
| reachable | ✗ | $x_{k+1} = 0 \cdot x_k + 0 \cdot u_k$ is not reachable, because no nonzero state can be reached from $0$. |