Home > mpt > @polytope > getInnerEllipsoid.m

# getInnerEllipsoid

## PURPOSE

GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope

## SYNOPSIS

function E = getInnerEllipsoid(Pset,E,Options)

## DESCRIPTION

```GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope

E = getInnerEllipsoid(Pset,x0,E,Options)

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DESCRIPTION
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This function computes he largest ellipsoid inscribed in a polytope.
It is also possible to pass an ellipsoid (x-x0) E (x - x0) <= rho and
to compute the maximum rho such that the scaled ellipsoid is still contained
in the polytope.

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INPUT
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Pset    -   Polytope object constraining the ellipsoid
E,x0    -   Optional: input ellipsoid with center x0, i.e.
(x-x0) E^(-1) (x - x0) <= rho
given as an ELLIPSOID object
The function then computes the maximum rho such that the
ellipsoid is still contained in Pset.
Options
.plotresult    - If problem is in 2D and flag is set to 1, the result
will be plotted (Default: 0).
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OUTPUT
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E       -   Maximum volume ellipsoid,  (x-x0) E (x - x0) <= 1, returned as
an ELLIPSOID object

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LITERATURE
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S. Boyd and L. Vanderberghe, Convex Optimization

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• plot PLOT Plots regions of the explicit controller
• set SET Set a field of MPTCTRL objects
• double DOUBLE Function used to access internal properties of the given polytope
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
• plot PLOT Plots polytopes in 2D or 3D
• set SET Used to modify internal properties of a given polytope object
• size SIZE Returns size of the given polytope object
• mpt_plotellip mpt_PLOTELLIP function to plot polytopes
This function is called by:

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