Home > mpt > extras > auxiliary > mpt_norm2pwa.m

# mpt_norm2pwa

## PURPOSE

MPT_NORM2PWA transformes a linear norm into an equivalent PWA fcn representation

## SYNOPSIS

function pwafcn = mpt_norm2pwa(P,l,Options)

## DESCRIPTION

 MPT_NORM2PWA  transformes a linear norm into an equivalent PWA fcn representation

pwafcn = mpt_norm2pwa(P,l,Options)

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DESCRIPTION
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Transformes a linear norm ||P*x||_l into an equivalent PWA function,
||P*x||_l =  pwafcn.Bi{i}*x + pwafcn.Ci{i}  for x \in pwafcn.Pn(i)

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INPUT
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P            - scaling matrix in ||P*x||_l
l            - = 1 or Inf, standard vector norm (l=Inf will be assumed if not
set)
Options      - optional arguments
.Pn        - one polytope over which the norm should be defined
.method    - if 1 (default) solution is found via enumeration
if 2 solution will be found via YALMIP [should be used for larger problems!]

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OUTPUT
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pwafcn       - descriptoin of the PWA function
.Bi,.Ci
.Pn       - polyhedral partition over which the PWA fcn is defined
.Pfinal   - domain of the PWA function
.epi      - implicit epigraph description of ||P*x||_l using sdvar.
(more efficient than the PWA description for computation)
(only existent if Options.method=1)

Note: for simple plotting use plot(pwafcn.epi)

see also  MPT_DLYAP_INFNORM   MPT_LYAPUNOV

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• 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
• 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
• set SET Used to modify internal properties of a given polytope object
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• unitbox UNITBOX Creates a unit box centered at origin
This function is called by:

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