I have a nonlinear state space model:
$$\dot{x} = f(x, u)$$
And I have linearize that with a Jacobian matrix.
Now I got a linear state space model:
$$\delta\dot{x} = A\delta x + B\delta u$$
But the problem is that some of the eigenvalues:
$$ det(sI - A) = 0 $$
are positive.
So then I solve $P$ from:
$$ AP + PA^T + B = 0$$
And put $P$ in:
$$V(x) = x^T P x $$
So, what is next step? I want to check if the system is stable in just some state position. How can I do that?