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3.6. H
2
AND H
∞
ANALYSIS AND SYNTHESIS 95
(rad/sec) ratio
-1.0000e+00 0.0000e+00 1.0000e+00 1.0000
-5.0000e-01 6.3048e+00 6.3246e+00 0.0791
-5.0000e-01 -6.3048e+00 6.3246e+00 0.0791
-1.0000e+01 0.0000e+00 1.0000e+01 1.0000
The order of the names in the systemname variable, must match the order of the rows in
the connections variable and the order of the last arguments in the sysic function call.
3.6 H
2
and H
∞
Analysis and Synthesis
This section discusses the synthesis functions available in Xµ.Aweighted
interconnection structure is set up so that either H
2
or H
∞
design methods can be
applied. This discussion assumes that the reader is familiar with the theory and
application of these methodologies. Section 2.3 gives a more detailed overview of the
theory and outlines the algorithms used in the calculations. For specific design examples
and further discussion refer to the demos given in Section 4.1.
3.6.1 Controller Synthesis
The generic synthesis interconnection structure is illustrated in Figure 3.5. The
objective is to design K(s) such that the closed loop interconnection is stable and the
resulting transfer function from w to e (denoted by G(s)) satisfies either an H
2
or H
∞
norm objective.
Xµ provide functions to calculate the controllers minimizing either the H
2
or H
∞
norm
of G(s); h2syn and hinfsyn respectively.
Recall from Section 2.3 that the minimizing H
2
norm controller (calculated by h2syn)is
unique. The format of this function is given below.
k = h2syn(p,nmeas,ncon)
The variable p is the open loop interconnection structure (P(s) in Figure 3.5). This