Routh Approximation

Given a high order stable transfer function G, this code would compute the reduced order equivalent model for the system using Routh Approximation (or Gamma-Delta Approximation) of required degree.

Refer : V. Krishnamurthy and V. Sheshadri, " A simple and direct method for reducing order of systems using routh approximations in frequency domain", IEEE Transactions on Automatic Control, Vol. 21, pp. 797-799, Oct. 1976.
Function

RouthApprox=Routh_Approximation(G,r)

Computes the r-th order Routh Approximation of a given n-th order
transfer function G, with 1<=r<=n.

Example
G=tf([1 2],[1 3 4 5])
r=2;
R=Routh_Approximation(G,r)

gives the output as

0.5714 s + 1.143
R= ---------------------
s^2 + 2.286 s + 2.857