# Documentation

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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.