The closed -loop transfer function can be expressed as a function of G(s)and H(s). From Fig. 2-2-1we write C(S=G(Sc(s) (2-2) B(S=H(SC(S) 2-3) The actuating signal is written C(S=R(S-B(S) Substituting eq(2-4 )into eq(2-2)yields C(S=G(SR(S-G(SB(S) Substituting eq(2-3)into eq(2-5)gives C(S=G(SR(S)G(SH(SC(S) 2-6) Solving C(s) from the last equation the closed-loop transfer function of the system is given by M(s)=C(S)R(s)=G(s)/(1+G(s)H(s) (2-7)The closed –loop transfer function can be expressed as a function of G(s) and H(s). From Fig.2-2-1we write: C(s)=G(s)c(s) (2-2) B(s)=H(s)C(s) (2-3) The actuating signal is written C(s)=R(s)-B(s) (2-4) Substituting Eq(2-4)into Eq(2-2)yields C(s)=G(s)R(s)-G(s)B(s) (2-5) Substituting Eq(2-3)into Eq(2-5)gives C(s)=G(s)R(s)-G(s)H(s)C(s) (2-6) Solving C(s) from the last equation ,the closed-loop transfer function of the system is given by M(s)=C(s)/R(s)=G(s)/(1+G(s)H(s)) (2-7)