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Worst-case norm of uncertain matrix

maxnorm = wcnorm(m) [maxnorm,wcu] = wcnorm(m) [maxnorm,wcu] = wcnorm(m,opts) [maxnorm,wcu,info] = wcnorm(m) [maxnorm,wcu,info] = wcnorm(m,opts)

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 *worst-case
norm* analysis. The maximum norm is called the *worst-case
norm*.

As with other *uncertain-system* analysis
tools, only bounds on the worst-case norm are computed. The exact
value of the worst-case norm is guaranteed to lie between these upper
and lower bounds.

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 worst-case norm, positive scalar. |

`UpperBound` | Upper bound on worst-case 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))

A third output argument provides information about sensitivities of the worst-case 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 worst-case uncertainty values. The fields
of |

`Sensitivity` | A `sys` .
Field values are positive numbers, each entry indicating the local
sensitivity of the worst-case norm in `maxnorm.LowerBound` to
all of the individual uncertain elements' uncertainty ranges.
For instance, a value of 25 indicates that if the uncertainty range
is increased by 8%, then the worst-case norm should increase by about
2%. If the `Sensitivity` property of the `wcOptions` object
is `'off'` , the values are `NaN` . |

| Same as `WorstPerturbation` . Included for
compatibility with R2016a and earlier. |

`ArrayIndex` | Same as `Model` . Included for compatibility
with R2016a and earlier. |

See `wcgain`

.

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