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.

Question

RICCARDO ZAVADLAL 2023-10-21

0
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https://ww2.mathworks.cn/matlabcentral/answers/2036686-hello-i-would-like-to-ask-help-to-solve-the-parametric-inequality-coming-out-after-applying-the-rou

回答： Aishwarya 2023-10-31

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

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

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 =

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Answer 1

Aishwarya 2023-10-31

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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