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State-space or transfer function plant augmentation for
use in weighted mixed-sensitivity *H*_{∞} and *H*_{2} loopshaping
design

P = AUGW(G,W1,W2,W3)

`P = AUGW(G,W1,W2,W3)`

computes
a state-space model of an augmented LTI plant * P*(

$$T{y}_{1}{u}_{1}\triangleq \left[\begin{array}{c}{W}_{1}S\\ {W}_{2}R\\ {W}_{3}T\end{array}\right]$$

where * S, R* and

$$\begin{array}{c}S={(}^{I}\\ R=K{(}^{I}\\ T=GK{(}^{I}\end{array}$$

The LTI systems * S* and

**Plant Augmentation**

For dimensional compatibility, each of the three weights *W*_{1}, *W*_{2} and *W*_{3} must
be either empty, a scalar (SISO) or have respective input dimensions *N*_{y}, *N*_{u},
and *N*_{y} where * G* is

`P = AUGW(G,W1,[],W3)`

is `W2`

).The transfer functions * G*,

`P`

will not be stabilizable by
any `K`

.The augmented plant * P*(

$$P(s)=\left[\begin{array}{cc}{W}_{1}& -{W}_{1}G\\ 0& {W}_{2}\\ 0& {W}_{3}G\\ I& -G\end{array}\right]$$

Partitioning is embedded via `P=mktito(P,NY,NU)`

,
which sets the InputGroup and OutputGroup properties of P as follows

[r,c]=size(P); P.InputGroup = struct('U1',1:c-NU,'U2',c-NU+1:c); P.OutputGroup = struct('Y1',1:r-NY,'Y2',r-NY+1:r);

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