I got this control system with such dynamics: \begin{equation} \dot{x}(t)=-\frac{\partial{H(x)}}{\partial{x}},~H\geq 0,~H(x)=0\Rightarrow x=0 \end{equation} $x(t)$ is a $n$-dimension vector, questions are: is this control system stable, if it is, how to find the balance point or points?
2026-04-01 16:27:01.1775060821
Is this system stable?
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Pick a candidate Lyapunov function $H(x)$ and see how far you can get. The equilibria are the points where $\frac{\partial H}{\partial x} = 0$, but everything depends on the properties of $H$, which you have not specified.