Continuous-time LTI case.
I have a problem getting the state matrix of this trajectory.
One element of the state matrix is known. $ A = \begin{pmatrix} a & 4 \\c & d \end{pmatrix} $
I know that one Eigenvalue is 0, $s_1 = 0$, and one Eigenvector is $p_1=\begin{pmatrix} 1\\1 \end{pmatrix}$.
With the equation $s_1 - a*p_{11} + s - 4*p_{12} = 0$, i get $a = -4$.
I also found out that $c=-d$.
But I am stuck now. I don't know how to get the other elements.
Is there more information to get from the image?
Help appreciated...
German version:
Für ein freies System 2. Ordnung der Form $\frac{dx}{dt} = A*x$ ist das dazugehörige Trajektorienbild gegeben.
Außerdem ist die zugehörige Systemmatrix A (teilweise) bekannt: $ A = \begin{pmatrix} a & 4 \\c & d \end{pmatrix} $ Bestimmen Sie die fehlenden Elemente der Systemmatrix A . (HINWEIS: Benützen Sie das angegebene Trajektorienbild!)
Translation:
The trajectory image associated with a free system of second order of the form $\frac{dx}{dt} = A*x$ is given. Further, the associated system matrix $A$ is (partially) known: $ A = \begin{pmatrix} a & 4 \\c & d \end{pmatrix} $ Determine the missing elements of the system matrix $A$. (HINT: Use the given trajectory image!)