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//caption:stability_using_Routh-hurwitz_criterion
//example 12.17
//page 530
s=%s;
syms K
G=sym('K/((s^3+3*s+2)*(s^2+6*s+24))');
H=1;
CH=((s^3+3*s+2)*(s^2+6*s+24)+K)
disp('=0',CH,"characterstics_eq,CH=")
c0=coeffs(CH,'s',0);
c1=coeffs(CH,'s',1);
c2=coeffs(CH,'s',2);
c3=coeffs(CH,'s',3);
c4=coeffs(CH,'s',4);
b=[c0 c1 c2 c3 c4 ]
routh=[b([5,3,1]);b([4,2]),0]
routh=[routh;-det(routh(1:2,1:2))/routh(2,1),routh(1,3),0]
routh(3,1)=simple(routh(3,1))
t=routh(2:3,1:2)
l=simple(-det(t)/t(2,1))
routh=[routh;l,0,0]
//routh=[routh;K,0,0]
disp(routh,"routh=")
disp("for given system to be stable,following condition should be satisfied");
disp("78.84-0.259K>0")
disp("which gives limiting value of K")
disp("K<288.9");
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