Learn more about Routh-Hurwitz stability criterion and its application in Wikipedia
I seperated the function into two main parts. One section operates when the number of coefficients are even and the other, when the number of coefficients are odd.
Test Example 1 : s^4 + 4s^3 + 5s^2 + 6s + 8 = 0
routh([1 4 5 6 8])
Routh-Hurwitz Table:
| C0 | C1 | C2 | C3 |
|---|---|---|---|
| S^4 | 1 | 5 | 8 |
| S^3 | 4 | 6 | 0 |
| S^2 | 3.5 | 8 | 0 |
| S^1 | -3.1429 | 0 | 0 |
| S^0 | 8 | 0 | 0 |
Number of Right Poles = 2
This function file is the optimized version of the first routh.m file.
- Even and odd coefficients sectiones are combined.
- Special conditions have been considered.
- One element in the first column is zero ( using Epsilon)
- All elements of a row are zero ( using auxiliary function)
Test Example 2 : s^4 + s^3 + s^2 + s + 1 = 0
routh([1 1 1 1 1])
Routh-Hurwitz Table:
| C0 | C1 | C2 | C3 |
|---|---|---|---|
| S^4 | 1 | 1 | 1 |
| S^3 | 1 | 1 | 0 |
| S^2 | 0.01 | 1 | 0 |
| S^1 | -99 | 0 | 0 |
| S^0 | 1 | 0 | 0 |
Number of Right Poles = 2
Test Example 3 : s^5 + s^4 + 2s^3 + 3s^2 + s + 2 = 0
routh([1 1 2 3 1 2])
Routh-Hurwitz Table:
| C0 | C1 | C2 | C3 |
|---|---|---|---|
| S^5 | 1 | 2 | 1 |
| S^4 | 1 | 3 | 2 |
| S^3 | -1 | -1 | 0 |
| S^2 | 2 | 2 | 0 |
| S^1 | 4 | 2 | 0 |
| S^0 | 2 | 0 | 0 |
Number of Right Poles = 2