Example · High school
Terms
| Term | This example | Why |
|---|
| lyapunov stable |
✓ |
|
| attractive |
✓ |
|
| asymptotically stable |
✓ |
|
| globally asymptotically stable |
✓ |
The origin of $\dot{x} = -x^3$ is globally asymptotically stable, and so Lyapunov stable and attractive, because every solution decreases in size to $0$.
|
| exponentially stable |
✗ |
|
| finite time stable |
✗ |
The origin of $\dot{x} = -x^3$ is not exponentially or finite-time stable, because solutions converge like $1 / \sqrt{2t}$, slower than every exponential.
|
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