is the Control
Design Block that represents an uncertain complex number.
The value of an uncertain complex number lies in a disc, centered
NominalValue, with radius specified by the
ucomplex element. The size of the disc can
also be specified by
Percentage, which means the
radius is derived from the absolute value of the
The properties of
Nominal value of element
Radius of disk
Additive variation (percent of
The simplest construction requires only a name and nominal value.
Displaying the properties shows that the default
and the default radius is 1.
a = ucomplex('a',2-j)
a = Uncertain complex parameter "a" with nominal value 2-1i and radius 1.
Name: 'a' NominalValue: 2.0000 - 1.0000i Mode: 'Radius' Radius: 1 Percentage: 44.7214 AutoSimplify: 'basic'
Sample the uncertain complex parameter at 400 values, and plot in the complex plane. Clearly, the samples appear to be from a disc of radius 1, centered in the complex plane at the value 2-j.
asample = usample(a,400); plot(asample(:),'o'); xlim([-0.5 4.5]); ylim([-3 1]);
The uncertain complex matrix class,
represents the set of matrices given by the formula
N + WLΔWR
where N, WL,
and WR are known matrices,
and Δ is any complex matrix with .
All properties of a
can be accessed with
The properties are
Nominal value of element
The simplest construction requires only a name and nominal value. The default left and right weight matrices are identity.
You can create a 4-by-3
and view its properties.
m = ucomplexm('m',[1 2 3;4 5 6;7 8 9;10 11 12]) Uncertain Complex Matrix: Name m, 4x3 get(m) Name: 'm' NominalValue: [4x3 double] WL: [4x4 double] WR: [3x3 double] AutoSimplify: 'basic' m.NominalValue ans = 1 2 3 4 5 6 7 8 9 10 11 12 m.WL ans = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
Sample the uncertain matrix, and compare to the nominal value. Note the element-by-element sizes of the difference are generally equal, indicative of the default (identity) weighting matrices that are in place.
abs(usample(m)-m.NominalValue) ans = 0.2948 0.1001 0.2867 0.3028 0.2384 0.2508 0.3376 0.1260 0.2506 0.2200 0.3472 0.1657
Change the left and right weighting matrices, making the uncertainty larger as you move down the rows, and across the columns.
m.WL = diag([0.2 0.4 0.8 1.6]); m.WR = diag([0.1 1 4]);
Sample the uncertain matrix, and compare to the nominal value. Note the element-by-element sizes of the difference, and the general trend that the smallest differences are near the (1,1) element, and the largest differences are near the (4,3) element, which is completely expected by choice of the diagonal weighting matrices.
abs(usample(m)-m.NominalValue) ans = 0.0091 0.0860 0.2753 0.0057 0.1717 0.6413 0.0304 0.2756 1.4012 0.0527 0.4099 1.8335