Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearSystems`
rd0DMcompute  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
θbar={θb11,θb12,θb13};
In[2]:=
system={{x11,x12,x13,x14,x15},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6},{y11,y12,z11,z12},{{0,1,0,θb11,0,2θb11,θb12,0,0,0,0,0,θb11},{0,0,1,0,0,0,0,0,0,0,0,0,0},{0,-θb13,0,0,0,0,0,0,0,0,0,0,0},{-1,0,0,-2,1,-θb11,-θb12,0,0,0,0,0,θb12},{0,0,0,-1/2,-1,0,0,0,0,0,0,0,θb12},{1,0,0,0,0,θb11,θb12,1,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,1,0,0,0,0},{1,0,0,0,0,θb11,θb12,0,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4,5,6,7,8},{1,2},{3,4}};
[system]
 | systemcheck |
Out[2]=
True
In[3]:=
 | EZDCFAD |
Out[3]=
0,{{θb11,θb12},{-θb12,θb11}},default,default,{{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1}},{x11,x12,x13,x14,x15},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6,y11,y12},{y11,y12,z11,z12},-+-+,1,0,θb11++,0,0,0,-+-+,+,0,0,0,θb11,+++,-+,{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,-θb13,0,0,0,0,0,0,0,0,0,0,0,0,0},-1++++,0,0,-2,1,0,0,+++,0,0,0,0,θb12,-+-+,0,0,0,0,-,-1,0,0,0,0,0,0,0,θb12,0,0,{1,0,0,0,0,θb11,θb12,1,0,0,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,1,0,0,0,0,0,0},{1,0,0,0,0,θb11,θb12,0,0,0,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,0,0,0,0,0,0,0},{1,2,9,10},{1,2},{1,2},{3,4,5,6,7,8},{1,2},{3,4}
2
2
θb11
2
θb11
2
θb12
2
θb12
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θb11
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θb12
θb11θb12
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θb11
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θb12
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2
θb11
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θb11
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θb12
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θb11
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θb12
θb11θb12
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θb11
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θb11
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θb11
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θb12
θb11θb12
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θb11
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θb11
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θb12
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θb11
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θb12
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θb11
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θb11
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θb12
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θb12
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θb11
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θb12
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θb11
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θb11
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θb12
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θb12
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θb11
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θb12
1
2
In[4]:=
{strictform1,systemobservable1,nO1,observabilityindices1,transformation1,systeminobservercanonicalform1}=
[system]
| strictobservercanonicalform |
State transformation is xold = transformation.xnew
Out[4]=
True,True,5,{3,2},{{1,0,0,0,0},{0,1,0,-θb11,0},{-θb13,0,1,0,-θb11},{0,0,0,1,0},{0,0,0,-1,1}},{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6},{y11,y12,z11,z12},{0,1,0,0,0,2θb11,θb12,0,0,0,0,0,θb11},{-θb11-θb13,0,1,-3θb11,0,-,-θb11θb12,0,0,0,0,0,θb11θb12},-θb11,0,0,-+θb11θb13,0,-+2θb11θb13,-θb11θb12+θb12θb13,0,0,0,0,0,2θb11θb12+θb11θb13,{-1,0,0,-3,1,-θb11,-θb12,0,0,0,0,0,θb12},-1,0,0,-,0,-θb11,-θb12,0,0,0,0,0,2θb12,{1,0,0,0,0,θb11,θb12,1,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,1,0,0,0,0},{1,0,0,0,0,θb11,θb12,0,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,0,0,0,0,0},{1,2},{1,2},{1,2},{3,4,5,6,7,8},{1,2},{3,4}
2
θb11
5θb11
2
2
θb11
5
2
In[5]:=
predesignmodel1=ExpandAll[systeminobservercanonicalform1/.{θb11θ11+1/2,θb12θ12+1/2,θb133θ13+1/2}]
Out[5]=
{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6},{y11,y12,z11,z12},0,1,0,0,0,1+2θ11,+θ12,0,0,0,0,0,+θ11,-1-θ11-3θ13,0,1,--3θ11,0,--θ11-,----θ11θ12,0,0,0,0,0,+++θ11θ12,--θ11,0,0,-1-2θ11++3θ11θ13,0,-+3θ13+6θ11θ13,--θ11θ12++3θ12θ13,0,0,0,0,0,++θ12+2θ11θ12++3θ11θ13,-1,0,0,-3,1,--θ11,--θ12,0,0,0,0,0,+θ12,-1,0,0,-,0,--θ11,--θ12,0,0,0,0,0,1+2θ12,1,0,0,0,0,+θ11,+θ12,1,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,1,0,0,0,0,1,0,0,0,0,+θ11,+θ12,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,0,0,0,0,0,{1,2},{1,2},{1,2},{3,4,5,6,7,8},{1,2},{3,4}
1
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1
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3θ13
2
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4
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θ11
θ11
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3θ13
2
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3θ11
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3θ13
2
1
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In[6]:=
predesignmodel1=ExpandAll[predesignmodel1/.{θ11^2θ14,θ11θ12θ15,θ11θ13θ16,θ12θ13θ17}]
Out[6]=
{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6},{y11,y12,z11,z12},0,1,0,0,0,1+2θ11,+θ12,0,0,0,0,0,+θ11,-1-θ11-3θ13,0,1,--3θ11,0,--θ11-θ14,----θ15,0,0,0,0,0,+++θ15,--θ11,0,0,-1-2θ11++3θ16,0,+3θ13-θ14+6θ16,-+-θ15+3θ17,0,0,0,0,0,++θ12++2θ15+3θ16,-1,0,0,-3,1,--θ11,--θ12,0,0,0,0,0,+θ12,-1,0,0,-,0,--θ11,--θ12,0,0,0,0,0,1+2θ12,1,0,0,0,0,+θ11,+θ12,1,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,1,0,0,0,0,1,0,0,0,0,+θ11,+θ12,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,0,0,0,0,0,{1,2},{1,2},{1,2},{3,4,5,6,7,8},{1,2},{3,4}
1
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In[7]:=
θ1={θ11,θ12,θ13,θ14,θ15,θ16,θ17}
Out[7]=
{θ11,θ12,θ13,θ14,θ15,θ16,θ17}
In[8]:=
designmodel1=
[predesignmodel1,θ1]
| rd0DMcompute |
State transformation is xold = transformation.xnew
Out[8]=
{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6,y11,y12},{y11,y12,z11,z12},0,1,0,0,0,1+2θ11,+θ12,0,0,0,0,0,+θ11,0,0,-1,0,1,-,0,--θ11+3θ11--θ12-+θ11(-θ11-3θ13)-θ14,--+3θ11+θ11--+θ12(-θ11-3θ13)-θ15,θ11+3θ13,3θ11,0,0,0,+++θ15,-θ11-3θ13,-3θ11,-,0,0,-1,0,+θ11+θ11+3θ13-θ14+6θ16---θ12-2θ11++3θ16,-+θ11+θ12+-θ15-+θ11-2θ11++3θ16+3θ17,θ11,2θ11--3θ16,0,0,0,++θ12++2θ15+3θ16,-θ11,-2θ11++3θ16,-1,0,0,-3,1,--θ11,--θ12,0,0,0,0,0,+θ12,0,0,-1,0,0,-,0,--θ11,--θ12,0,0,0,0,0,1+2θ12,0,0,1,0,0,0,0,+θ11,+θ12,1,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,1,0,0,0,0,0,0,1,0,0,0,0,+θ11,+θ12,0,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,0,0,0,0,0,0,0,{1,2},{1,2},{1,2},{3,4,5,6,7,8,9,10},{1,2},{3,4}
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In[9]:=
designmodel1=ExpandAll[designmodel1]
Out[9]=
{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6,y11,y12},{y11,y12,z11,z12},0,1,0,0,0,1+2θ11,+θ12,0,0,0,0,0,+θ11,0,0,-1,0,1,-,0,--2θ11+-3θ11θ12++3θ11θ13-θ14,-++3-+θ11θ12++3θ12θ13-θ15,θ11+3θ13,3θ11,0,0,0,+++θ15,-θ11-3θ13,-3θ11,-,0,0,-1,0,-+-2θ11θ12++-θ14++3θ12θ16,θ11+2+θ11θ12+--θ15--3θ11θ16+3θ17,θ11,2θ11--3θ16,0,0,0,++θ12++2θ15+3θ16,-θ11,-2θ11++3θ16,-1,0,0,-3,1,--θ11,--θ12,0,0,0,0,0,+θ12,0,0,-1,0,0,-,0,--θ11,--θ12,0,0,0,0,0,1+2θ12,0,0,1,0,0,0,0,+θ11,+θ12,1,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,1,0,0,0,0,0,0,1,0,0,0,0,+θ11,+θ12,0,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,0,0,0,0,0,0,0,{1,2},{1,2},{1,2},{3,4,5,6,7,8,9,10},{1,2},{3,4}
1
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3θ12θ13
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15θ16
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θ11
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3θ11θ13
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In[10]:=
designmodel1=ExpandAll[designmodel1/.{θ11^2θ14,θ11θ12θ15,θ11θ13θ16,θ12θ13θ17}]
Out[10]=
{x1,x2,x3,x4,x5},{u11,u12,wg1,wg2,wg3,wg4,wg5,wg6,y11,y12},{y11,y12,z11,z12},0,1,0,0,0,1+2θ11,+θ12,0,0,0,0,0,+θ11,0,0,-1,0,1,-,0,--2θ11+-3θ15+3θ16,-+-++3θ14+3θ17,θ11+3θ13,3θ11,0,0,0,+++θ15,-θ11-3θ13,-3θ11,-,0,0,-1,0,-+-2θ15++3θ12θ16+,θ11++2θ14-3θ16-3θ11θ16+3θ17,θ11,2θ11--3θ16,0,0,0,++θ12++2θ15+3θ16,-θ11,-2θ11++3θ16,-1,0,0,-3,1,--θ11,--θ12,0,0,0,0,0,+θ12,0,0,-1,0,0,-,0,--θ11,--θ12,0,0,0,0,0,1+2θ12,0,0,1,0,0,0,0,+θ11,+θ12,1,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,1,0,0,0,0,0,0,1,0,0,0,0,+θ11,+θ12,0,0,0,0,0,0,0,0,0,0,0,1,0,--θ12,+θ11,0,0,0,0,0,0,0,0,{1,2},{1,2},{1,2},{3,4,5,6,7,8,9,10},{1,2},{3,4}
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θ11
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15θ13
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15θ16
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3θ17
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In[11]:=
designmodel1=ExpandAll[designmodel1/.{θ11θ16θ18,θ12θ16θ19}]