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# range

## PURPOSE

RANGE Affine transformation of a polytope

## SYNOPSIS

function R=range(P,A,f,Options)

## DESCRIPTION

RANGE Affine transformation of a polytope

[R]=range(P,A,f,Options)

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DESCRIPTION
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R=range(P,A,f) computes affine transformation of a polytope
affine mapping m: x |-> A*x + f maps polytope P to R, m: P -> R;
i.e.,   R={x(1) | x(0) \in P, x(1)=Ax(k)+f}

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INPUT:
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P                - Polytope
A,f              - system dynamics matrices; x(k+1)=Ax+f; A needs to be
invertible.
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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R   - polytope; See DESCRIPTION for details.

see also DOMAIN

## 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
• length LENGTH Returns number of elements in a polytope array
• polytope POLYTOPE Default constructor for the POLYTOPE object
• range RANGE Affine transformation of a polytope
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
This function is called by:
• mtimes MTIMES Polytope multiplication
• range RANGE Affine transformation of a polytope
• mpt_reachSets MPT_REACHSETS Computes sets of reachable states for a given system / controller
• mpt_reachXU MPT_REACHXU One-step reachability computation for an affine system

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