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 ^

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