This document contains a MATLAB program that performs stability analysis using the Routh-Hurwitz criterion. It allows the user to input the coefficients of a characteristic equation and analyzes the stability of the system based on the signs of the resulting Routh array. The program displays the number of roots in each quadrant of the s-plane and whether the system is stable, unstable, or marginally stable based on the Routh array calculations. It also provides options for the user to rerun the analysis or clear variables and end the program.

1. ROOT LOCUS (SAMPLE ASSIGNMENT)
Our online Tutors are available 24*7 to provide Help with Root Locus Homework/Assignment or a
long term Graduate/Undergraduate Root Locus Project. Our Tutors being experienced and proficient
in Root Locus ensure to provide high quality Root Locus Homework Help. Upload your Root Locus
Assignment at ‘Submit Your Assignment’ button or email it to .
You can use our ‘Live Chat’ option to schedule an Online Tutoring session with our Root Locus
Tutors.
Routh Hurwitz Criterion
RouthHurwitzCriterion.m
% PROGRAM BY ASUTOSH MISHRA %
clc;
close all;
clear all;
y1 = input('Press "y" and "Enter" to Start The Program:: ','s');
disp(' ');
if (y1~='y')
errordlg('**Please Type "y" to continue Else The Program Will Terminate**','Caution');
y1 = input('Press "y" and Enter to Continue:: ','s');
end
if (y1~='y')
disp(' ');
disp('Program Terminates');
end
y2 = y1;
y3 = y1;
clc;
while (y1=='y') && (y2=='y')
if (y3~='y')
clc;
end
disp('~:~:~:~:~:~:~:~:~:~ROUTH HURWITZ CRITERION~:~:~:~:~:~:~:~:~:~');
disp(' ');
disp(' Stability Analysis Using Characteristic Equation ');
disp(' ');
if (y1=='y');
clear a b c D1 D2 G G1 G2 H i I k K L1 L2 m n P P1 P2 Q r R R1 R2 R3 Z Z1;
disp('~:~:Analysis Using Characteristic Equation:~:~');
disp(' ');
helpdlg(sprintf('--> The Charateristic Equation Is " a(0) * x^n + a(1) * x^(n-1) + ... + a(n)"
n--> a(0) , a(1) , a(2) ... are coefficients n--> If n is odd then Even Power Coefficients are
:: a(1) , a(2) , a(3) ... a(n-1) n--> If n is even then the Even Power Coefficients are :: a(0) ,
info@assignmentpedia.com

2. a(2) , ... a(n) n--> Give The values of all the Coefficients(Even if they are "0") n'),'Note On
Entering Input');
a = input('Even Power Coefficients in decreasing order of power of "x"(Ex. Within []) :: ');
b = input('Odd Power Coefficients in decreasing order of power of "x"(Ex. Within []) :: ');
disp(' ');
digits(5)
L1 = length(a);
L2 = length(b);
disp(['No. Of The Roots:: ',num2str(L1+L2-1)]);
disp(' ');
disp('~:~:~:~:~:~:~:~:~:~:~:~Routh Array~:~:~:~:~:~:~:~:~:~:~:~');
if (L2>L1)
P = 0;
P1 = 0;
P2 = 0;
Z = zeros(1,(L2-L1));
R = horzcat(a,Z);
Z1 = horzcat(a,Z);
R1 = b;
disp(vpa(b));
disp(vpa(Z1));
H = 1;
for n = 1:(L2+L1-2)
R2 = R;
for m = 1:(L2-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)

3. H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);
else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;
end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R));
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end

4. end
end
disp(' ');
disp(['Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-P1-1-P2)]);
disp(['Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
else
if (L1>L2)
P = 0;
P1 = 0;
P2 = 0;
Z = zeros(1,(L1-L2));
R = horzcat(b,Z);
Z1 = horzcat(b,Z);
R1 = a;
disp(vpa(a));
disp(vpa(Z1));
H = 1;
for n = 1:(L1+L2-2)
R2 = R;
for m = 1:(L1-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)
H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);

5. else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = (r');
for j = 1:length(R3)
if (real((R3(1,j)))<0.0001)
P2 = P2+1;
end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R));
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
disp(' ');
disp(['The Roots Of The Auxiliary Eqn. are:: ',num2str(R3)]);
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end
end
end

6. disp(' ');
disp(['Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-1-P1-P2)]);
disp(['Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
end
end
if (L1 == L2)
P = 0;
P1 = 0;
P2 = 0;
H = 1;
for h = 1:(L1-1)
Q(1,h) = (((a(1,1).*b(1,h+1))-(b(1,1).*a(1,h+1)))./(a(1,1)));
end
L3 = length(Q);
T = a;
if (Q(1,1)==0)&&(Q(1,h)==0)
for j = 1:(length(a)+length(b)-1)
if (rem(j,2)~=0)
Q(1,j) = T(1,(j+1)./2);
else
Q(1,j) = 0;
end
end
r = roots(Q);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;
end
end
K = polyder(Q);
I = 2:4:(length(K)*2);
K(:,(I+2)./2) = [];
G2 = zeros(1,length(b)-length(K));
Q = horzcat(K,G2);
end
if (Q(1,1)<0)
P = P+1;
P1 = P1+1;
end
P3 = 0;
Z = zeros(1,(L2-L3));
R = horzcat(Q,Z);
Z1 = horzcat(Q,Z);

7. R1 = a;
Z0 = zeros(1,(length(Z1)-L1));
D1 = horzcat(a,Z0);
D2 = horzcat(b,Z0);
disp(vpa(D2));
disp(vpa(D1));
disp(vpa(Z1));
for n = 1:(L1+L2-3)
R2 = R;
for m = 1:(L1-1)
if (R2(1,1)~=0)
if (abs(R2(1,1))~=inf)
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
else
R2(1,1) = 1;
R(1,m) = (((R2(1,1).*R1(1,m+1))-(R1(1,1).*R2(1,m+1)))./(R2(1,1)));
end
else
if (R2(1,1)==0)
R(1,m) = R1(1,m+1);
if ((R1(1,1)*R2(1,2))>R1(1,2))
R(1,1) = -(1./0);
P1 = P1+1;
else
R(1,1) = (1./0);
end
end
end
end
if (R(1,1)==0)&&(R(1,m)==0)
H = R(1,1);
for i = 1:L1+L2-n
if (rem(i,2)~=0)
G(1,i) = R2(1,(i+1)./2);
else
if (rem(i,2)==0)
G(1,i) = 0;
end
end
end
r = roots(G);
R3 = r';
for j = 1:length(R3)
if (real(R3(1,j))<0.0001)
P2 = P2+1;

8. end
end
k = polyder(G);
i = 2:4:(length(k)*2);
k(:,(i+2)./2) = [];
G1 = zeros(1,length(R2)-length(k));
R = horzcat(k,G1);
end
if (R(1,1)<0)
P = P+1;
end
if (R2(1,1)*R(1,1)<0)
P1 = P1+1;
end
disp(vpa(R))
R1 = R2;
R2 = R;
end
if (P>0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Unstable~:~:~:~:~:~:~');
else
if (P==0) && (H==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Marginally Stable~:~:~:~:~:~:~');
disp(' ');
disp(['The Roots Of The Auxiliary Equations Are:: ',num2str(R3)])
else
if (P==0)
disp(' ');
disp('~:~:~:~:~:~:~The System is Stable~:~:~:~:~:~:~')
end
end
end
disp(' ');
disp(['Effective no. of Roots to the right of imaginary axis in Z-plane:: ',num2str(P1)]);
disp(['Effective no. of Roots to the left of imaginary axis in Z-plane:: ',num2str(L1+L2-
P1-1-P2)]);
disp(['Effective no. of Roots on the imaginary axis in Z-plane:: ',num2str(P2)]);
end
else
.....
end
disp(' ');
y2 = input('Do you want to Rerun Program again?(y/n):: ','s');

9. if (y2~='y')&&(y2~='n')
disp(' ');
disp('Please Type "y" or "n"');
disp(' ');
y2 = input('Do you want to Rerun Program again?(y/n):: ','s');
end
if (y2=='y')
y3 = input('Do you want to keep the previous analysis?(y/n):: ','s');
if (y3~='y')&&(y3~='n')
disp(' ');
disp('Please Type "y" or "n"');
disp(' ');
y3 = input('Do you want to keep the previous analysis?(y/n):: ','s');
end
end
end
if (y2=='n')
disp(' ');
disp('Program Terminated');
disp(' ');
disp('*****You can "Press Any Key" to clear screen and "End Program"*****');
pause
pause on;
clc;
end
visit us at www.assignmentpedia.com or email us at info@assignmentpedia.com or call us at +1 520 8371215