Section 7.1 The Feature of Integrating Systems Internal Stability The closed-loop system is internally stable if and only if all elements in the transfer matrix H(s)are stable: [图]=[周] where G(s)C(s) G(s) H(s)= 1+ G(s)C(s) 1+G(s)C(s) C(s) G(s)C(s) 1+G(s)C(s) 1+G(s)C(s) Since the Youla parameterization for stable plants cannot be used for integrating plants,the following transfer function is defined: Q(s)= C(s) 1+G(s)C(s) 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 4/79Section 7.1 The Feature of Integrating Systems Internal Stability The closed-loop system is internally stable if and only if all elements in the transfer matrix H(s)are stable:  y(s) u(s)  = H(s)  r(s) d 0 (s)  where H(s) =     G(s)C(s) 1 + G(s)C(s) G(s) 1 + G(s)C(s) C(s) 1 + G(s)C(s) −G(s)C(s) 1 + G(s)C(s)     Since the Youla parameterization for stable plants cannot be used for integrating plants, the following transfer function is defined: Q(s) = C(s) 1 + G(s)C(s) Zhang, W.D., CRC Press, 2011 Version 1.0 4/79