National Instruments 370757C-01, NI MATRIX Xmath Robust Control Module - page 34

Chapter 3 SystemEvaluation
© National Instruments Corporation 3-5 MATRIXx Xmath Robust Control Module
•If A has an imaginary eigenvalue at jω0, linfnorm( ) returns:
vOMEGA =
SIGMA = Infinity
where ω0 is one of the imaginary eigenvalues of A.
•Even if H is unstable, linfnorm( ) returns its maximum singular
value on the jω axis.
For discrete-time systems linfnorm( ) converts a discrete-time L∞
norm computation problem to a continuous-time problem using a Cayley
transformation. For example, it maps the unit circle conformally onto the
complex right half plane using a linear fractional transformation. The
linfnorm( ) function then calls itself to solve the continuous-time
problem, and finally converts the solution back to discrete-time.
Example 3-2 Example of linfnorm()
Sys=system([-0.2,-1;1,0],[1,0]',[0,1],0);
[sigma,omega]=linfnorm(Sys)
sigma (a scalar) = 5.07322
omega (a scalar) = 0.157081
The linfnorm( ) function will return the L∞ norm (sigma) of the transfer
matrix H(jω) described by Sys, and omega is the vector of frequencies
where it is achieved. linfnorm( ) computation can be checked by
plotting the singular values of H(jω) as a function of ω (Figure 3-2).
sv=svplot(Sys,{fmin=.01, fmax=1.0});
ω0