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Results tagged with stability
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user 77927
Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)
3
votes
Nonlinear ODE system: stability
Another approach would be to expand in series form around some equilibrium point, and observe whether the lower order terms resemble some "known" behaviour, which is known as a normal form on the cent …
- 274
3
votes
1
answer
98
views
Examples of systems with stable equilibria at the boundary of the phase space
Hopfield networks are gradient dynamical systems, used (among other things) to solve combinatorial optimization problems, because stable equilibria are at vertices of the hypercube $[-1,1]^n$. They ha …
- 274
2
votes
Accepted
Show that 0 is Lyapunov stable by using the given Hamiltonian $H(z)$ as a Lyapunov-function
With your setting, it seems you are right and this cannot be a Lyapunov function, but I cannot check the original paper, which could have some relevant context. Note that different authors provide sli …
- 274
2
votes
Accepted
Quadratic stability of linear time varying system
Sure: take the scalar ODE $\dot x=-x$, with $A=-1$, which is exponentially stable and the state transition matrix is $\Phi(t)=e^{-t}$ (i.e. $x(t)=\Phi(t) x_0$). Assume $Q=e^{2t}$, which is not bounded …
- 274