Solution 9.10.3.4 S G a = a G @G @a = a Ka s(s +a) @ @a Ka s(s +a) = s(s +a) K  ;Kas s 2 (s+ a) 2 + K s(s+ a)  = s(s +a) " ;as+ s 2 +as s 2 (s+ a) 2 # = s (s+ a) S T c a = a T c @T c @a = a Ka s 2 + as+ Ka @ @a Ka s 2 + as+ Ka = s 2 + as+ Ka K  ;Ka(s+K) (s 2 +as +Ka) 2 + K s 2 + as+ Ka  = s 2 + as+ Ka 1  ;a(s+ K) (s 2 +as +Ka) 2 + 1 s 2 + as+ Ka  = (s 2 + as+Ka)) " ;as;Ka+s 2 + as+ Ka (s 2 +as+ Ka) 2 # = s 2 s 2 + as+ Ka S G K = K G @G @K = K Ka s(s +a) @ @K Ka s(s +a) = s(s +a) a  a s(s +a)  = 1 S T c K = K T c @T c @K = K Ka s 2 + as+ Ka @ @K Ka s 2 + as+ Ka = s 2 + as+ Ka a  ;Ka(a) (s 2 +as +Ka) 2 + a s 2 + as+ Ka  = s 2 + as+ Ka 1  ;Ka (s 2 +as +Ka) 2 + 1 s 2 + as+ Ka  = (s 2 + as+Ka)) " ;Ka+s 2 + as+ Ka (s 2 + as+Ka) 2 # = s(s +a) s 2 + as+ Ka