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[v, vOPTD] = optscale (M, {tol})

The 

optscale( )

 function optimally scales a matrix. An iterative 

optimization (ellipsoid) algorithm which calculates upper and lower 
bounds on the left side of Equation 2-5 is used. If these bounds are within 
a relative accuracy you have specified 

(tol)

, 

optscale( )

 stops. 

optscale( )

 also will stop and issue a warning if the maximum number 

of iterations is reached:

optscale( )

 will find a 

μ(M) no larger than 

pfscale( )

.

In some cases, the uncertain transfer functions can be divided into groups 
that do not interact. This is illustrated in Figure 2-9.

Figure 2-9.  Non-Interacting Uncertain Transfer Functions

As you can see, 

δ

3

 does not affect the stability margin at all because there 

is no feedback through it. The system in Figure 2-9 can be reduced to the 
two separate systems shown in Figure 2-10. The stability margin of 
Figure 2-9 is the minimum of the stability margins of the systems in 
Figure 2-10.

200

rows(M)

×

δ

2

δ

3

δ

1

δ

4