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# lmireg

Specify LMI regions for pole placement

## Syntax

```region = lmireg
region = lmireg(reg1,reg2,...)
```

## Description

lmireg is an interactive facility to specify the LMI regions involved in multi-objective H synthesis with pole placement constraints (see msfsyn). Recall that an LMI region is any convex subset D of the complex plane that can be characterized by an LMI in z and , i.e.,

$D=\left\{z\in C:L+Mz+{M}^{T}\overline{z}<0\right\}$

for some fixed real matrices M and L = LT. This class of regions encompasses half planes, strips, conic sectors, disks, ellipses, and any intersection of the above.

Calling lmireg without argument starts an interactive query/answer session where you can specify the region of your choice. The matrix region = [L, M] is returned upon termination. This matrix description of the LMI region can be passed directly to msfsyn for synthesis purposes.

The function lmireg can also be used to intersect previously defined LMI regions reg1, reg2,.... The output region is then the [L, M] description of the intersection of these regions.