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# aff2pol

Convert affine parameter-dependent models to polytopic models

## Syntax

```polsys = aff2pol(affsys)
```

## Description

aff2pol derives a polytopic representation polsys of the affine parameter-dependent system

 $E\left(p\right)\stackrel{˙}{x}=A\left(p\right)x+B\left(p\right)u$ (2-1)
 $y=C\left(p\right)x+D\left(p\right)u$ (2-2)

where p = (p1, . . . , pn) is a vector of uncertain or time-varying real parameters taking values in a box or a polytope. The description affsys of this system should be specified with psys.

The vertex systems of polsys are the instances of Equation 2-1 and Equation 2-2 at the vertices pex of the parameter range, i.e., the SYSTEM matrices

$\left(\begin{array}{cc}A\left({p}_{ex}\right)+jE\left({p}_{ex}\right)& B\left({p}_{ex}\right)\\ C\left({p}_{ex}\right)& D\left({p}_{ex}\right)\end{array}\right)$

for all corners pex of the parameter box or all vertices pex of the polytope of parameter values.