Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`NonlinearSystems`
NLKarmanDecomposition  |
| {ncbo,ncbob,nco,ncob,transformation,resultsystem}=KarmanDecomposition[nlsystem,x0] computes the Karman decomposition of the nonlinear system: nlsystem x0 nlsystem nlsystem x0 | |
Examples
(1)
Basic Examples
(1)
In[1]:=
system={{x1,x2,x3,x4,x5},{u1,u2},{y1,y2},{{-1,1,0,0,0,1,-1},{1,-1,0,0,1,-1,0},{0,0,1,0,0,0,0},{1,0,0,0,0,1,0},{0,0,0,0,0,0,0},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}}
Out[1]=
{{x1,x2,x3,x4,x5},{u1,u2},{y1,y2},{{-1,1,0,0,0,1,-1},{1,-1,0,0,1,-1,0},{0,0,1,0,0,0,0},{1,0,0,0,0,1,0},{0,0,0,0,0,0,0},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}}
In[2]:=
 | NLKarmanDecomposition |
 | convert2NLsystem |
State transformation is xnew = transformation[xold] and transformation is a pure function; One may attach the inverse transformation as the third element in type, which must also be a pure function.
Out[2]=
{1,1,2,1,{x5,x3,x1,x2,x4},{{x11,x21,x31,x41,x51},{u1,u2},{y1,y2},{Function[{x11,x21,x31,x41,x51,u1,u2},{0,x21,u1-u2-x31+x41,-u1+x11+x31-x41,u1+x31}],Function[{x11,x21,x31,x41,x51,u1,u2},{x31,x41}]},{1,2},{1,2},{1,2},{},{1,2},{}}}
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