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Posted on Wednesday, 11 April 2012


The Routh-Hurwitz stability criterion is a necessary method to establish the stability of linear time invariant (LTI) control system.

More generally, given a polynomial, some calculations using only the coefficients of that polynomial can lead us to the conclusion that it is not stable.

In this program you give your system coefficents and the Routh-Hurwitz table would be shown



clc
clear
r=input('input vector of your system coefficents: ');
m=length(r);
n=round(m/2);
q=1;
k=0;
for p = 1:length(r) 
    if rem(p,2)==0
        c_even(k)=r(p); 
    else
        c_odd(q)=r(p); 

        k=k+1;
        q=q+1;
    end
end
a=zeros(m,n); 

if m/2 ~= round(m/2)
    c_even(n)=0;
end
a(1,:)=c_odd;
a(2,:)=c_even;
if a(2,1)==0
    a(2,1)=0.01;
end
for i=3:m
    for j=1:n-1
        x=a(i-1,1);
        if x==0
            x=0.01;
        end

        a(i,j)=((a(i-1,1)*a(i-2,j+1))-(a(i-2,1)*a(i-1,j+1)))/x;

    end
    if a(i,:)==0
        order=(m-i+1);
        c=0;
        d=1;
        for j=1:n-1
            a(i,j)=(order-c)*(a(i-1,d));
            d=d+1;
            c=c+2;
        end
    end
    if a(i,1)==0
        a(i,1)=0.01;
    end
end
Right_poles=0;
for i=1:m-1
    if sign(a(i,1))*sign(a(i+1,1))==-1
        Right_poles=Right_poles+1;
    end
end
fprintf('\n Routh-Hurwitz Table:\n')
a
fprintf('\n Number Of Right Poles =%2.0f\n',Right_poles)

reply = input('Do You Need Roots of System? Y/N ', 's');
if reply=='y'||reply=='Y'
    ROOTS=roots(r);
    fprintf('\n Given Polynomials Coefficents Roots :\n')
    ROOTS
else
end

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