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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");