The objective of this section is to find a suitable mapping that permits the analysis and synthesis of a MIMO control system by a set of equivalent MISO control systems. This mapping results in m2 equivalent systems, each with two inputs and one output. One input is designated as a "desired" input and the other as an "unwanted" input (cross-coupling effects and/or external system disturbances). First, Eq. (5.23) is pre-multiplied by [I + PG] to obtain
FGPTGPI = + ][ (5.27)
When P is nonsingular, then pre-multiplying both sides of this equation by P−1 yields
FGTGP = + ][ 1− (5.28)
which puts the constrained or the structured parametric uncertainty in one place in the equation. Let
p ... pp
. . .