Compute conic-sector index of linear system

`RX = getSectorIndex(H,Q)`

`RX = getSectorIndex(H,Q,tol)`

`RX = getSectorIndex(H,Q,tol,fband)`

```
[RX,FX]
= getSectorIndex(___)
```

```
[RX,FX,W1,W2,Z]
= getSectorIndex(___)
```

`DX = getSectorIndex(H,Q,dQ)`

`DX = getSectorIndex(H,Q,dQ,tol)`

computes
the relative index `RX`

= getSectorIndex(`H`

,`Q`

)`RX`

for the linear system `H`

and
the conic sector specified by `Q`

. When `RX`

<
1, all output trajectories *y*(*t*)
= *Hu*(*t*) lie
in the sector defined by:

$${\int}_{0}^{T}y{\left(t\right)}^{T}Q\text{\hspace{0.17em}}y\left(t\right)dt}<0,$$

for all *T* ≥ 0.

`getSectorIndex`

can also check whether all
I/O trajectories {*u*(*t*),*y*(*t*)} of
a linear system *G* lie in the sector defined by:

$${\int}_{0}^{T}{\left(\begin{array}{c}y\left(t\right)\\ u\left(t\right)\end{array}\right)}^{T}Q\text{\hspace{0.17em}}\left(\begin{array}{c}y\left(t\right)\\ u\left(t\right)\end{array}\right)dt}<0,$$

for all *T* ≥ 0.
To do so, use `getSectorIndex`

with ```
H
= [G;I]
```

, where `I = eyes(nu)`

, and `nu`

is
the number of inputs of `G`

.

For more information about sector bounds and the relative index, see About Sector Bounds and Sector Indices.

computes
the index in the direction specified by the matrix `DX`

= getSectorIndex(`H`

,`Q`

,`dQ`

)`dQ`

.
If `DX`

> 0, then the output trajectories of `H`

fit
in the conic sector specified by `Q`

. For more
information about the directional index, see About Sector Bounds and Sector Indices.

The directional index is not available if `H`

is
a frequency-response data (`frd`

) model.

`getPassiveIndex`

| `getPeakGain`

| `getSectorCrossover`

| `nyquist`

| `sectorplot`