Home > mpt > @polytope > intersect.m

# intersect

## PURPOSE

INTERSECT Intersection of 2 polytopes or polytope arrays

## SYNOPSIS

function [R,fulldim] = intersect(P1,P2,Options)

## DESCRIPTION

```INTERSECT Intersection of 2 polytopes or polytope arrays

R = intersect(P1,P2,Options)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
Returns normalized minimal representation of intersection of input
arguments

USAGE:
R=intersect(P1,P2)
R=intersect(P1,P2,Options)

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INPUT
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P1,P2   - Polytopes or polyarrays, where a polyarray is considered as
the union of polytopes

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OUTPUT
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R - Polytope containing the intersection of input polytopes

Note: INTERSECT and AND have different functionality.

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• dimension DIMENSION Returns dimension of the given polytope
• end END Returns the last element in a given polytope array
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• length LENGTH Returns number of elements in a polytope array
• mldivide MLDIVIDE Set difference
• polytope POLYTOPE Default constructor for the POLYTOPE object
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
This function is called by:
• extreme EXTREME Calculates extreme points of a given polytope
• plot PLOT Plots polytopes in 2D or 3D
• mpt_getCommonSOSLyapFct MPT_GETCOMMONSOSLYAPFCT Calculates Common SOS Lyapunov function for system with additive disturbance
• mpt_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
• mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver6 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_optControlPWA MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

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