wcnorm
Worstcase norm of uncertain matrix
Syntax
maxnorm = wcnorm(m) [maxnorm,wcu] = wcnorm(m) [maxnorm,wcu] = wcnorm(m,opts) [maxnorm,wcu,info] = wcnorm(m) [maxnorm,wcu,info] = wcnorm(m,opts)
Description
The norm of an uncertain matrix generally depends on the values of its uncertain elements. Determining the maximum norm over all allowable values of the uncertain elements is referred to as a worstcase norm analysis. The maximum norm is called the worstcase norm.
As with other uncertainsystem analysis tools, only bounds on the worstcase norm are computed. The exact value of the worstcase norm is guaranteed to lie between these upper and lower bounds.
Basic syntax
Suppose mat
is a umat
or a
uss
with M uncertain elements. The results
of
[maxnorm,maxnormunc] = wcnorm(mat)
maxnorm
is a structure with the following fields.
Field  Description 

LowerBound  Lower bound on worstcase norm, positive scalar. 
UpperBound  Upper bound on worstcase norm, positive scalar. 
maxnormunc
is a structure that includes values of uncertain
elements and maximizes the matrix norm. There are M field names,
which are the names of uncertain elements of mat
. The value of
each field is the corresponding value of the uncertain element, such that when
jointly combined, lead to the norm value in maxnorm.LowerBound
.
The following command shows the norm:
norm(usubs(mat,maxnormunc))
Basic syntax with third output argument
A third output argument provides information about sensitivities of the worstcase norm to the uncertain elements ranges.
[maxnorm,maxnormunc,info] = wcnorm(mat)
The third output argument info
is a structure with the
following fields:
Field  Description 

Model  Index of model with largest gain (when

WorstPerturbation  Structure of worstcase uncertainty values. The fields
of 
Sensitivity  A 
 Same as WorstPerturbation . Included for
compatibility with R2016a and earlier. 
ArrayIndex  Same as Model . Included for compatibility
with R2016a and earlier. 
Examples
Algorithms
See wcgain
.