Remove LMI from system of LMIs

newsys = dellmi(lmisys,n)

`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.

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 *X*_{2} 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.

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