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2.1. INTRODUCTION 7
Figure 2.1: The generic robust control model structure
Trace(M) trace of M (
n
i=1
M
ii
)
Block diagrams will be used to represent interconnections of systems. Consider the
example feedback interconnection shown in Fig. 2.1. Notice that P has been partitioned
into four parts. This diagram represents the equations,
z = P
11
v + P
12
u
y = P
21
v + P
22
u
v =∆z.
This type of diagram (and the associated equations) will be used whenever the objects
P, z, y, etc., are well defined and compatible. For example P could be a matrix and z,
y, etc., would be vectors. If P represented a dynamic system then z, y, etc., would be
signals and
y = P
21
v + P
22
u,