Mu Analysis and Synthesis Toolbox

Find the norm or peak norm of a VARYING matrix

Syntax

• [peak,indv,index] = pkvnorm(matin,p) 
  out = (matin) 
  out = (matin,p)
  

Description
pkvnorm sweeps through the independent variable, calculating the norm of each matrix as specified by the input argument p, following the convention from MATLAB's norm command. The default for p is the largest singular value of matin. The three output arguments all pertain to the peak and its location: peak value, peak, the independent variable's value, indv, and the independent variable's index, index.

vnorm is a VARYING matrix version of MATLAB's norm command. The operation of the norm command is identical to vnorm, except that vnorm also works on CONSTANT and VARYING matrices, which produces a CONSTANT or VARYING output. vnorm returns the matrix out with its norm at each independent variable value.

Examples
The two-input/two-output VARYING matrix matin has its independent variable at 0.2 and 0.6. The vnorm command finds the largest singular value of the VARYING matrix at each value of the indepedent variable. pkvnorm returns the largest singular value of the VARYING matrix, its independent variable value, and the index of the independent variable.

• minfo(matin)
  varying:2 pts2 rows2 cols
  see(matin)
  2 rows2 columns
  indep variable 0.2
   1.0000      0
   0           0.5000
  indep variable 0.6
   4           0
  -5           1
  nrm = vnorm(matin,2); 
  see(nrm)
  1 row    1 column
  indep variable 0.2
    1
  indep variable 0.6
    6.4510
  [peak,indv,index] = pkvnorm(matin); 
  peak
  peak =
    6.4510
  indv
  indv =
    0.6000
  index
  index ==
    2
  

Algorithm
pkvnorm and vnorm call the MATLAB norm command.

See Also
norm, vsvd

pck, pss2sys, sys2pss, unpck

ric_eig