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## Routh's array in symbolic way

version 1.41.0.0 (1.27 KB) by Carlos M. Velez S.

### Carlos M. Velez S. (view profile)

Routh's array of symbolic polinomials. It is different for similar functions in Matlab Central.

Updated 13 Oct 2015

[M L] = routh_hurwitz(P,N)
This function gives the Routh's array from a numerical or SYMBOLIC polynomial and includes two special cases: (1) the first element of the row is zero; (b) a row of zeros.
P Numerical or symbolic array of coeficients. In the case of symbolic variables it is necesarry to define them as: >> syms a b c ...
N Digits to be considered zero a number. E.g, for N=5, 10^(-5) is considered a zero. By default, N=10
M Routh's array without any simplification (e.g., with epsilon notation)
L Simplified first column of Routh's array with simplification (e.g., using the limit when epsilon tends to zero) that determines the number of roots in the right-half of the s-plane: the number of changes of signs in L
Examples:
1. [M, L]=routh_hurwitz([1 0 2 3 4])
2. syms a b c d K; [M, L]=routh_hurwitz([1 b c d+a*K])
3. syms k; [M, L]=routh_hurwitz([1 k 1 1])
4. [M, L]=routh_hurwitz([1 -3 -15 -9 -58 12 72])
5. syms a; [M, L]=routh_hurwitz([1 0 2 3 a])

Developed by Carlos M. Vélez S., cmvelez@eafit.edu.co
http://sistemascontrol.wordpress.com/
EAFIT University, http://www.eafit.edu.co
Medellín, Antioquia, Colombia
November 24th 2011

### Cite As

Carlos M. Velez S. (2020). Routh's array in symbolic way (https://www.mathworks.com/matlabcentral/fileexchange/33926-routh-s-array-in-symbolic-way), MATLAB Central File Exchange. Retrieved .

begum sariguzel

### begum sariguzel (view profile)

I had "not enough input argument" error. What the reason could be?

Humam Al-Baidhani

Nicely done!

arghya thengal

### arghya thengal (view profile)

quite useful and handy!

Noman Khan

### Noman Khan (view profile)

Kindly help me, this function worked perfectly last week, Now its shows busy, I do not know, how it will work again. Thanks

Cris

### Cris (view profile)

I apllied thia script and is usefull

 13 Oct 2015 1.41.0.0 The function "limit" is used instead of "subs" function 1 Dec 2011 1.4.0.0 It was fixed the problem when the last elements of a polynomial are zeros. 30 Nov 2011 1.1.0.0 The input argument N was included
##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux