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//determining critical value of K
s=%s
syms K
m=s^3+10*s^2+(K+21)*s+13*K
cof_a_0 = coeffs(m,'s',0);
cof_a_1 = coeffs(m,'s',1);
cof_a_2 = coeffs(m,'s',2);
cof_a_3 = coeffs(m,'s',3);
r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
n=length(r);
routh=[r([4,2]);r([3,1])];
routh=[routh;-det(routh)/routh(2,1),0];
t=routh(2:3,1:2); //extracting the square sub block of routh matrix
routh=[routh;-det(t)/t(2,1),0]
disp(routh,"rouths tabulation=")
routh(3,1)=0 //For marginaly stable system
disp("for its closed loop poles more negetive than -1")
s=%s
syms K
m=s^3+7*s^2+(K+4)*s+12*K-12
cof_a_0 = coeffs(m,'s',0);
cof_a_1 = coeffs(m,'s',1);
cof_a_2 = coeffs(m,'s',2);
cof_a_3 = coeffs(m,'s',3);
r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
n=length(r);
routh=[r([4,2]);r([3,1])];
routh=[routh;-det(routh)/routh(2,1),0];
t=routh(2:3,1:2); //extracting the square sub block of routh matrix
routh=[routh;-det(t)/t(2,1),0]
disp(routh,"rouths tabulation=")
routh(3,1)=0 //For marginaly stable system
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