Accelerating the pace of engineering and science

# 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.