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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`
strictobservercanonicalform
​
{strictform,systemobservable,nO,observabilityindices,transformation,systeminobservercanonicalform}=strictobservercanonicalform[system]
tests the observability of the pair (a,c) and returns
True
if the pair is observable in
systemobservable
.
nO
equals the dimension of the observable subspace, and
observabilityindices
is the list of observability indices of the outputs. The pair (a,c) is that for the
system
with the active outputs as the output. It further tests whether the pair (a,c) admits the strict observer canonical form, that is, after the coordinate transformation into observer canonical form, the nonvanishing columns of the matrix c are columns of the identity matrix. If so,
strictform
=
True
, and the state transformation is given in transformation. If not so,
strictform
=
False
, and transformation = transformation of observabilityQandindices[a,c]. The result of the transformed system is returned in
systeminobservercanonicalform
.
​
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]:=
{strictform,systemobservable,nO,observabilityindices,transformation,systeminobservercanonicalform}=
strictobservercanonicalform
[system]
State transformation is xold = transformation.xnew
Out[2]=
{True,True,3,{1,2},{{1,0,0},{0,1,0},{2,-3,1}},{{x11,x21,x31},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,2,0,0,0,0,1},{0,-4,1,1,1,1,0},{-5,-9,0,2,4,4,-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}}}
SeeAlso
observercanonicalform
 
▪
observabilityQandindices
 
▪
uniformobservabilityindices
 
▪
strictOCFAD
RelatedGuides
▪
Guide for ZigangPan`LinearSystems`
""

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