Appendix 13.1: Derivation of the Relative Gain for an n-Input–n-Output System
The relative gain between input j and output i is defined as
Output i is the following steady-state function of all of the inputs:
The relationship between input j and output i with all other inputs constant is
For any desired output vector, y, we can find the corresponding input vector, u, from
Defining Ĝ(0)=G-1(0)=K-1
The relationship between all outputs and input ...
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