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FGP

Fig. 5.6 MIMO control structure two-by-two system (2x2).

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

. . .