Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

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`