# dellmi

Remove LMI from system of LMIs

## Syntax

```newsys = dellmi(lmisys,n)
```

## Description

`dellmi` deletes the n-th LMI from the system of LMIs described in `lmisys`. The updated system is returned in `newsys`.

The ranking `n` is relative to the order in which the LMIs were declared and corresponds to the identifier returned by `newlmi`. Since this ranking is not modified by deletions, it is safer to refer to the remaining LMIs by their identifiers. Finally, matrix variables that only appeared in the deleted LMI are removed from the problem.

## Examples

Suppose that the three LMIs

`$\begin{array}{l}{A}_{1}^{T}{X}_{1}+{X}_{1}{A}_{1}+{Q}_{1}<0\\ {A}_{2}^{T}{X}_{2}+{X}_{2}{A}_{2}+{Q}_{2}<0\\ {A}_{3}^{T}{X}_{3}+{X}_{3}{A}_{3}+{Q}_{3}<0\end{array}$`

have been declared in this order, labeled `LMI1`, `LMI2`, `LMI3` with `newlmi`, and stored in `lmisys`. To delete the second LMI, type

```lmis = dellmi(lmisys,LMI2) ```

`lmis` now describes the system of LMIs

`$\begin{array}{l}{A}_{1}^{T}{X}_{1}+{X}_{1}{A}_{1}+{Q}_{1}<0\\ {A}_{3}^{T}{X}_{3}+{X}_{3}{A}_{3}+{Q}_{3}<0\end{array}$`

and the second variable X2 has been removed from the problem since it no longer appears in the system.

To further delete `LMI3` from the system, type

```lmis = dellmi(lmis,LMI3) ```

or equivalently

```lmis = dellmi(lmis,3) ```

Note that the system has retained its original ranking after the first deletion.

## Version History

Introduced before R2006a