Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearSystems`
observabilityQandindices  |
| {systemobservable,nO,observabilityindices,transformation}=observabilityQandindices[a,c] a c | |
Examples
(1)
Basic Examples
(1)
In[1]:=
a={{1}};c={};
[a,c]
 | observabilityQandindices |
Out[1]=
{False,0,{},{{1}}}
In[2]:=
a={};c={};
[a,c]
| observabilityQandindices |
Out[2]=
{True,0,{},{}}
In[3]:=
a={{1,1,2,0,0,0},{1,1,1,1,0,0},{-1,1,0,0,1,0},{0,0,0,0,0,1},{-1,-1,2,0,0,1},{-2,2,0,0,1,0}};c={{1,0,0,0,0,0},{0,0,0,1,0,0}};
[a,c]
| observabilityQandindices |
Out[3]=
True,6,{3,3},{1,0,0,0,0,0},,-,-,,,,1,,,-2,-,-,{0,0,0,1,0,0},,,,-,-,-,,0,0,-,1,0
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3
1
3
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1
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3
1
3
1
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1
3
8
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5
3
2
3
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3
In[4]:=
a=Table[RandomInteger[{-1,1}],{i,6},{j,6}];c=Table[RandomInteger[{0,1}],{i,2},{j,6}];
[a,c]
| observabilityQandindices |
Out[4]=
True,6,{6,0},,-,,-,-,-,-,,-,-,-,-,,-,,-,-,-,-,,,,,,,-,,,,,-,,-,,,
15
22
13
33
5
66
3
22
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23
66
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29
132
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132
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132
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91
264
1
264
5
88
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264
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264
25
264
17
264
35
264
1
88
43
264
59
264
127
264
103
264
5
264
31
264
19
264
67
264
139
264
17
66
13
66
4
33
5
33
2
33
17
66
In[5]:=
tr=Out[48]〚4〛
Out[5]=
,-,,-,-,-,-,,-,-,-,-,,-,,-,-,-,-,,,,,,,-,,,,,-,,-,,,
15
22
13
33
5
66
3
22
4
33
23
66
7
44
29
132
17
132
3
44
19
132
15
44
91
264
1
264
5
88
5
264
13
264
25
264
17
264
35
264
1
88
43
264
59
264
127
264
103
264
5
264
31
264
19
264
67
264
139
264
17
66
13
66
4
33
5
33
2
33
17
66
In[6]:=
Inverse[tr].a.tr
Out[6]=
{{-1,1,0,0,0,0},{0,0,1,0,0,0},{-1,0,0,1,0,0},{11,0,0,0,1,0},{10,0,0,0,0,1},{-6,0,0,0,0,0}}
In[7]:=
c.tr
Out[7]=
{{1,0,0,0,0,0},{1,0,0,0,0,0}}
""