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# union

## PURPOSE

UNION convex union computation

## SYNOPSIS

function [Pu,how] = union(Pn, Options)

## DESCRIPTION

```UNION convex union computation

[Pu,how]=union(Pn,Options)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
This function tries to compute convex union of polytopes in the given polytope
array Pn

USAGE:
U = union([P1 P2 P3 ...])
U = union([P1 P2 P3 ...], Options)
[U,how] = union([P1 P2 P3 ...], Options)

NOTE! if Pn has more than 2 elements, the "convex union" problem is in fact
solved with polytope/isconvex.m, unless Options.useisconvex=0 is specified.

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INPUT
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Pn                  - Polytope array
Options.useisconvex - if enabled, uses isconvex() to compute convex union.
if number of regions is smaller than 3 and this flag is
not defined, the default value will be 0. otherwise, it
will be set to 1.

Options.lpsolver  - solver used for LP problems
Options.verbose   - level of verbosity
Options.abs_tol   - absolute tolerance

Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used

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OUTPUT
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Pu       - polytope describing convex union in case such one exists, return
array of input arguments otherwise
how = 1    if union is convex
= 0    union is not convex (in this case Pu=Pn)

see also ENVELOPE, HULL, ISCONVEX```

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• double DOUBLE Function used to access internal properties of the given polytope
• end END Returns the last element in a given polytope array
• isconvex ISCONVEX Checks if a polytope array forms a convex union
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• length LENGTH Returns number of elements in a polytope array
• polytope POLYTOPE Default constructor for the POLYTOPE object
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
This function is called by:
• or OR Convex union of n polytopes
• mpt_infsetPWA MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems
• mpt_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
• mpt_greedyMerging MPT_GREEDYMERGING Greedy merging of polyhedra
• mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
• mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

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