$[0, 1]$, for $\dot{x} = u$ with $\abs{u} \leq 1$
Terms
| Term | This example | Why |
|---|---|---|
| controlled invariant | ✓ | $[0, 1]$ is controlled invariant because the input $u = 0$ keeps solutions in place. |
| forward invariant | ✗ | $[0, 1]$ is not forward invariant for every input, because $u = 1$ pushes solutions out through $1$. |