Find the range of K for the stability of a unit-feedback control system whose loop transfer function is G(s) = K /s(s+1)(s+2) Solution Take characteristic equation 1+G(s)H(s) = 0 1+ k/s(s+1)(s+2) = 0 s(s+1)(s+2) +k = 0 s3 + 3s2 + 2s + k = 0 s3 1 2 s2 3 k s1 (6-k)/3 s0 k Now k>0 and (6-k)/3 > 0 so 0.