```python
import numpy as np
import sympy as sy
```


```python
s,z = sy.symbols('s,z', real=False)
l_1, l_2 = sy.symbols('l1, l2')
```


```python
Phi = sy.Matrix([[1.13, 0.52], [0.52, 1.13]])
Gamma = sy.Matrix([[0.13],[0.52]])
L = sy.Matrix([[l_1, l_2]])

M = z*sy.Matrix.eye(2) - (Phi - Gamma*L)
M
```




    Matrix([
    [0.13*l1 + z - 1.13,     0.13*l2 - 0.52],
    [    0.52*l1 - 0.52, 0.52*l2 + z - 1.13]])




```python
chPoly = sy.poly(M.det(), z)
chPoly
```




    Poly(1.0*z**2 + (0.13*l1 + 0.52*l2 - 2.26)*z + 0.1235*l1 - 0.52*l2 + 1.0065, z, domain='RR[l1,l2]')




```python
chDesired = sy.simplify(sy.expand((z-np.exp(-0.5))**2))

sol = sy.solve((chPoly - chDesired).coeffs(), [l_1, l_2])
```


```python
sol
```




    {l1: 1.61072237375216, l2: 1.61066302305182}




```python

```

548cbc7d9a2dd207b75419b6fccd6530f33261c5
ipynb
Jupyter Notebook
misc-notebooks/MR2007-final-exam-fall-2017.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2020-11-07T05:20:37.000Z
2020-12-22T09:46:13.000Z
misc-notebooks/MR2007-final-exam-fall-2017.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2020-06-12T20:44:41.000Z
2020-06-12T20:49:00.000Z
misc-notebooks/MR2007-final-exam-fall-2017.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2019-09-25T20:02:23.000Z
2019-09-25T20:02:23.000Z
Qwen/Qwen-72B
1. YES
2. YES