```python
import numpy as np
import sympy as sp
```


```python
a,b,c,d = sp.symbols('a, b, c, d')
w = sp.symbols('w')
s = sp.symbols('s')
h = sp.symbols('h')
A = sp.Matrix([[0, w], [-w, 0]])
I2 = sp.Matrix([[1, 0], [0, 1]])
B = sp.Matrix([[a,b],[c,d]])
B.inv()
```




    Matrix([
    [1/a + b*c/(a**2*(d - b*c/a)), -b/(a*(d - b*c/a))],
    [          -c/(a*(d - b*c/a)),      1/(d - b*c/a)]])




```python
As = (s*I2-A)
As
```




    Matrix([
    [s, -w],
    [w,  s]])




```python
Asinv = As.inv()
sp.pretty_print(Asinv)
```

    ⎡          2                ⎤
    ⎢1        w           w     ⎥
    ⎢─ - ───────────  ──────────⎥
    ⎢s      ⎛     2⎞    ⎛     2⎞⎥
    ⎢     2 ⎜    w ⎟    ⎜    w ⎟⎥
    ⎢    s ⋅⎜s + ──⎟  s⋅⎜s + ──⎟⎥
    ⎢       ⎝    s ⎠    ⎝    s ⎠⎥
    ⎢                           ⎥
    ⎢     -w              1     ⎥
    ⎢  ──────────       ──────  ⎥
    ⎢    ⎛     2⎞            2  ⎥
    ⎢    ⎜    w ⎟           w   ⎥
    ⎢  s⋅⎜s + ──⎟       s + ──  ⎥
    ⎣    ⎝    s ⎠           s   ⎦



```python
sp.LaplaceTransform?
```


```python
A*A*A
```




    Matrix([
    [   0, -w**3],
    [w**3,     0]])




```python
As =
```

7ce48fc3b1e1704f7c04c40d27d02fc1d8523777
ipynb
Jupyter Notebook
introduction/notebooks/Sampling-state-space-model-example.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2020-11-07T05:20:37.000Z
2020-12-22T09:46:13.000Z
introduction/notebooks/Sampling-state-space-model-example.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2020-06-12T20:44:41.000Z
2020-06-12T20:49:00.000Z
introduction/notebooks/Sampling-state-space-model-example.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