Hello, I would like to ask help to solve the parametric inequality coming out after applying the Routh Hurwitz criterion and plot the the solution as in the picture.

The problem is that i cannot find a similar command "isolate" for inequalities, i would like to plot the solutions of the variable a,b as in the picture. THe code is the following, i just need a few lines more to complete but i dont have ideas anymore. THanks

clc
clear all
syms a b
D= [1+b+a, 2*(1-b), -a+1+b]; % parametric polynomial (1+b+a)s^2+2*(1-b)*s+-a+1+b
l=length(D)

l = 3

syms m
if mod(l,2)==0
    m=sym(zeros(l,l/2));
    
    [cols,rows]=size(m);
    for i=1:rows
        m(1,i)=D(1,(2*i)-1);
        m(2,i)=D(1,(2*i));
    end
else
    m=sym(zeros(l,(l+1)/2));
    
    [cols,rows]=size(m);
    for i=1:rows
        m(1,i)=D(1,(2*i)-1);
    end
    for i=1:((l-1)/2)
        m(2,i)=D(1,(2*i));
    end
end
for j=3:cols
    
    if m(j-1,1)==0
        m(j-1,1)=0.001;
    end
    
    for i=1:rows-1
        m(j,i)=(-1/m(j-1,1))*det([m(j-2,1) m(j-2,i+1);m(j-1,1) m(j-1,i+1)]);
    end
end
disp('--------The Routh-Hurwitz array is:--------'), simplify(m)

--------The Routh-Hurwitz array is:--------

ans = 

% --------------------End of Bulding array--------------------------------
%{
% Checking for sign change
Temp=sign(m);a=0;
for j=1:cols
    a=a+Temp(j,1);
end
if a==cols
    disp('          ----> System is Stable <----')
else
    disp('          ----> System is Unstable <----')
end
%}
h=m(:,1);
for i=1:1:length(h)
    isolate(h(i)==0,b)
end

ans = 

ans = 

ans = 

Answer 1

[Aishwarya]

Hi,

I understand that you are looking to plot the inequalities obtained through your code in order to resemble the graph shown in the question. After reviewing the above code, I have provided an example code that will plot the inequalities and achieve the desired graph.

a = -5:0.01:5;  
b = -5:0.01:5;  

% Create 2-D grid coordinates  
[A, B] = meshgrid(a,b); 

% Create a 2-D grid which satisfy the inequalities 
ineq = (B > -A - 1) & (B < 1) & (B > A - 1); 

% Plot the points which satisfy equations 
ineq = double(ineq); 
ineq(ineq==0) = NaN; 
h = pcolor(A,B,double(ineq)); 
h.EdgeColor = 'none'; 
grid on 

Please refer to the MathWorks documentations below for more information about the functions used:

• pcolor” function: https://www.mathworks.com/help/matlab/ref/pcolor.html
• “Meshgrid” function: https://www.mathworks.com/help/matlab/ref/meshgrid.html

I hope this helps!