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Routh's array in symbolic way

version (1.27 KB) by Carlos M. Velez S.
Routh's array of symbolic polinomials. It is different for similar functions in Matlab Central.


Updated 13 Oct 2015

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[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
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.,
EAFIT University,
Medellín, Antioquia, Colombia
November 24th 2011

Cite As

Carlos M. Velez S. (2020). Routh's array in symbolic way (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (5)

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

Nicely done!

quite useful and handy!

Noman Khan

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


I apllied thia script and is usefull


The function "limit" is used instead of "subs" function

It was fixed the problem when the last elements of a polynomial are zeros.

The input argument N was included

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux