I have a control system problem, which ends up in that the eigenvalues of the system matrix should have a negative real part, then the system is stable.

The system matrix is real but not symmetric. The values depend on the system parameters, but zeros will remain zeros and equal value will be equal.

```
M =
-126.49961 41.887902 1120.2778 13417.173 - 175.32356
-41.887902 - 126.49961 - 13417.173 1120.2778 - 28.050364
0.1282520 0. - 3.4974646 0. 0.5473535
0. 0.1282520 0. - 3.4974646 0.0875722
5.63488 0.9015356 - 153.66458 - 24.585101 0.
```

This one is fine, all eigenvalues have negative real part.

However, there is a disturbance that adds up:

```
Me =
- 308.54625 - 49.364927 0. 0. 0.
- 49.364927 - 7.8979926 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
```

One pair of eigenvalues of (M + Me) has positive real part.

Now, I can add a compensation like

```
Mc =
- r - x 0. 0. 0.
x - r 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
```

here with r = 85.41 and x = 41.88

and (M + Me + Mc) again has eigenvalues with negative real part if r and x are high enough.

The question is: How can I find sufficient values for r and x without numerically calculating the matrix eigenvalues? Is there some approximation?

Thanks for any hint Alexander