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LinearSystems

Guides

  • Guide for ZigangPan`LinearSystems`

Symbols

  • calculaterelativedegree
  • controllabilityQandindices
  • controllercanonicalform
  • detectabilityQ
  • DTLyapunovequation
  • DTRiccatiequation
  • dynamicextension
  • emptyLTIsystem
  • EZDCFAD
  • EZDCF
  • gainsystem
  • generalizedRiccatiequationHM
  • linearLyapunovequation
  • observabilityQandindices
  • observercanonicalform
  • rd0DMcompute
  • Riccatiequation
  • simulationLTIsystem
  • stablizabilityQ
  • strictobservercanonicalform
  • strictOCFAD
  • systemblockdiagonal
  • systemcheck
  • systemconcatenate
  • systemfeedback
  • systemoperation
  • systemparallel
  • uniformobservabilityindices
  • ZDCF
ZigangPan`LinearSystems`
systemparallel
​
systemparallel
[
system
1
,
system
2
]
returns a composite system whose inputs are the joined list of inputs of
system1
and
system2
excluding the active inputs of
system2
, which were assumed to be equal to the active inputs of
system1
, and outputs are the joined list of outputs of
system1
and
system2
. Note that the active inputs of
system1
and
system2
must admit the same categorization (each element in active inputs are both control inputs or both disturbance inputs for both systems). See illustration below.
​
​
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
system={{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,2,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-2,-3,-1,1,1,1},{1,0,0,0,0,1,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}};
In[2]:=
system1={{x1},{u1,u2,w},{y,z},{{-1,1,0,1},{1,0,0,1},{1,0,0,0}},{1,2},{1},{1,2},{3},{1},{2}}
Out[2]=
{{x1},{u1,u2,w},{y,z},{{-1,1,0,1},{1,0,0,1},{1,0,0,0}},{1,2},{1},{1,2},{3},{1},{2}}
In[3]:=
systemoperation

systemparallel
[system,system1],{"View"};
Active
a1
a2
Type
s1
s2
s3
s4
c1
c2
d1
d2
d3
names
x11
x21
x31
x12
u1
u2
w1
w2
w
s1
x11
-1
2
0
0
0
0
0
1
0
s2
x21
-2
-1
1
0
1
1
1
0
0
s3
x31
-1
-2
-3
0
-1
1
1
1
0
s4
x12
0
0
0
-1
1
0
0
0
1
a1
m1
y1
1
0
0
0
0
0
1
0
0
a2
m2
y2
0
1
0
0
0
0
0
1
0
c1
z1
1
0
0
0
0
0
0
0
0
c2
z2
0
1
0
0
0
0
0
0
0
a3
m3
y
0
0
0
1
0
0
0
0
1
c3
z
0
0
0
1
0
0
0
0
0
SeeAlso
systemcheck
 
▪
systemblockdiagonal
 
▪
systemconcatenate
 
▪
systemfeedback
""

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