Timeline for Show that 0 is Lyapunov stable by using the given Hamiltonian $H(z)$ as a Lyapunov-function
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19 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2017 at 15:10 | vote | accept | Cahn | ||
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| Aug 17, 2015 at 14:39 | comment | added | Cahn | I will try this and see if I can get something. In my case I have to prove that every point on the $y_1$-Axis "goes" to the origin. | |
| Aug 17, 2015 at 14:36 | comment | added | Cahn | Thank you for your answer. I looked at "Semi-Definte Lyapunov functions stability and stabilizability" by Chabour and Kalitine, see at math.univ-metz.fr/~chabour/Articles/… It states at Theorem 1: If in a nbh U of the origin there existis a $C^1$ function $V:U \to \mathbb{R}^+$ such that: i. $V(x) \geq 0$ for all $x \in U$, $V(0)=0$. ii. $\dot V(x) \leq 0$ for all $x \in U$. iii. The origin is asymptotically stable wrt $Y_0=\{x \in U : V(x)=0 \}$ then the origin is a Lyapunov stable equilibrium point for the system. | |
| Aug 17, 2015 at 12:02 | comment | added | Piyush Grover | look for papers on "positive semi-definite lyapunov functions". | |
| Aug 17, 2015 at 11:41 | answer | added | Miguel | timeline score: 2 | |
| Aug 14, 2015 at 14:36 | review | First posts | |||
| Aug 14, 2015 at 15:17 | |||||
| Aug 14, 2015 at 14:34 | history | asked | Cahn | CC BY-SA 3.0 |