Compute or plot sector index as function of frequency

`sectorplot(`

plots
the relative sector indices for the dynamic system `H`

,`Q`

)`H`

and
a given sector matrix `Q`

. These indices measure
by how much the sector bound is satisfied (index less than 1) or violated
(index greater than 1) at a given frequency. (See About Sector Bounds and Sector Indices for
more information about the meaning of the sector index.) `sectorplot`

automatically
chooses the frequency range and number of points based on the dynamics
of `H`

.

Let the following be an orthogonal decomposition of the symmetric
matrix `Q`

into its positive and negative parts.

$$Q={W}_{1}{W}_{1}^{T}-{W}_{2}{W}_{2}^{T},\text{\hspace{1em}}{W}_{1}^{T}{W}_{2}=0.$$

The sector index plot is only meaningful if $${W}_{2}^{T}H$$ has a proper stable inverse. In that case, the sector indices are the singular values of:

$$\left({W}_{1}^{T}H\left(j\omega \right)\right){\left({W}_{2}^{T}H\left(j\omega \right)\right)}^{-1}.$$

`sectorplot(`

plots
the sector index for frequencies specified by `H`

,`Q`

,`w`

)`w`

.

If

`w`

is a cell array of the form`{wmin,wmax}`

, then`sectorplot`

plots the sector index at frequencies ranging between`wmin`

and`wmax`

.If

`w`

is a vector of frequencies, then`sectorplot`

plots the sector index at each specified frequency.