mpt_checkLyapFct

MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct

 for PWQ Lyapunov functions:
   islyapfun = mpt_checkLyapFct(ctrlStruct,LQ,LL,LC,Options)

 for PWA Lyapunov functions:
   islyapfun = mpt_checkLyapFct(ctrlStruct,LL,LC,Options)

 for Polynomial Lyapunov functions:
   islyapfun = mpt_checkLyapFct(ctrlStruct,V,Options)

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 DESCRIPTION
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 Grids the state-space into given number of points and for each state
 checks if decay rate of PWQ(PWA) Lyapunov function is negative.

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 INPUT
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 ctrl               - Explicit controller (MPTCTRL object)
 LQ,LL,LC           - Parameters of the PWQ(PWA) Lyapunov function
 Options.gridpoints - Number of grid points (if not provided, 30 is default)
 Options.N          - Number of simulation steps (5 by default)
 Options.verbose    - Level of verbosity
 Options.Pfinal     - polytope defining part of the state-space which should
                      be considered for cost computation. (only reasonable
                      if ctrlStruct.Pfinal is an empty polytope)

 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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 islyapfun - 1 if the function satifies criterions put on Lyapunov-type
             functions (positivity and negative decay rate); 0 otherwise
 XC        - matrix of data points (row-wise)
 decayrate - vector of decay rates corresponding to rows of XC

 see also MPT_GETPWQLYAPFCT. MPT_GETPWALYAPFCT