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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(s) with weighting functions W_{1}(s), W_{2}(s), and W_{3}(s) penalizing the error signal, control signal and output signal respectively (see block diagram) so that the closed-loop transfer function matrix is the weighted mixed sensitivity
$$T{y}_{1}{u}_{1}\triangleq \left[\begin{array}{c}{W}_{1}S\\ {W}_{2}R\\ {W}_{3}T\end{array}\right]$$
where S, R and T are given by
$$\begin{array}{c}S={(}^{I}\\ R=K{(}^{I}\\ T=GK{(}^{I}\end{array}$$
The LTI systems S and T are called the sensitivity and complementary sensitivity, respectively.
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 N_{y}-by-N_{u}. If one of the weights is not needed, you may simply assign an empty matrix [ ]; e.g., P = AUGW(G,W1,[],W3) is P(s) as in the Algorithms section below, but without the second row (without the row containing W2).
The transfer functions G, W_{1}, W_{2} and W_{3} must be proper, i.e., bounded as $$s\to \infty $$ or, in the discrete-time case, as $$z\to \infty $$. Additionally, W_{1}, W_{2} and W_{3} should be stable. The plant G should be stabilizable and detectable; else, P will not be stabilizable by any K.