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# mtimes

## PURPOSE

MTIMES Polytope multiplication

## SYNOPSIS

function R=mtimes(P,Q,Options)

## DESCRIPTION

```MTIMES Polytope multiplication

MTIMES Polytop multiplication

---------------------------------------------------------------------------
DESCRIPTION
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Three cases could happen:
1. Multiplication of two polytopes P1*P2 leads to a higher dimensional
polytope [H1 0; 0 H2] <= [K1; K2]
2. Multiplication of a polytope by a matrix -- this leads an affine
transformation performed by range.m
3. Multiplication of a polytope by a scalar -- if the origin is included
in the polytope, the polytope will be shrinked

USAGE:
R = P1*P2
R = P1*[1 0; 1 1]
R = P1*alfa

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INPUT
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P     - polytope / scalar / matrix
Q     - polytope / scalar / matrix
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OUTPUT
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R     - resulting polytope```

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• end END Returns the last element in a given polytope array
• isminrep ISMINREP Checks if a given polytope is in minimal representation
• isnormal ISNORMAL Checks if a given polytope is in normalized description
• length LENGTH Returns number of elements in a polytope array
• normalize NORMALIZE Normalizes a given polytope
• polytope POLYTOPE Default constructor for the POLYTOPE object
• range RANGE Affine transformation of a polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• size SIZE Returns size of the given polytope object
This function is called by:

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