Closed-loop transfer function matrix

From the partitioned matrix in equation (9.161), the closed-loop transfer function matrix relating yi and uj is... 

The closed-loop transfer function matrix (TFM) is given by... 

The objective of the H2 or Hqo control algorithms is to design a controller K that minimizes the H2 or Hoo norm of the closed-loop transfer function matrix, H, from the disturbance to the output vector. By definition, the H2 norm of a stable transfer function matrix is... 

Equation (15.64) gives the effects of setpoint and load changes on tbe controlled variables in the closedloop multivariable environment. The matrix (of order N X N) multiplying the vector of setpoints is the closedloop servo transfer function matrix. The matrix (N x 1) multiplying the load disturbance is the closed-loop regulator transfer function vector. 

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