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for all diagonal 

Δ such that

where 

μ(

.

) is the structured singular value, introduced by Doyle in 

[Doy82]. Thus, the margin is the inverse of the structured singular value of 
H

 diagonally scaled by the magnitude bounds. 

There is no numerically efficient algorithm that is guaranteed to compute 
μ(M), and hence the stability margin. However, it is possible to compute 
various good approximations to 

μ(M). One of these approximations is often 

exact.

A popular but conservative method uses singular values:

(2-4)

Plotting the right side of Equation 2-4 gives a lower bound on the 
actual stability margin. To get this plot, specify 

smargin( )

 with 

scaling="SVD"

. This approximation can be very conservative, meaning 

that the left side can be much larger than the right side. This fact spurred 
the study of structured singular values and the other approximations 
discussed in the following sections. 

For this example, you will use the system in Figure 2-3. This time 

smargin( )

 will be invoked with 

scaling="SVD"

, so 

smargin( )

 

will calculate Equation 2-4.

margSVD = smargin(H,delb,{scaling="SVD"});

Δ

α

≤

(

) }

1

μ M

( )

-------------

=

margin

ω

( )

1

σ

( )

----------------------

≥