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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`
strictOCFAD
​
{strictform,systemobservable,nO,observabilityindices,transformation,systeminobservercanonicalform}=strictOCFAD[system]
will extended the
system
with dummy state variables such that the extended system is in strict observer canonical form.
strictform
= True.
systemobservable
is True if the original system (as well as the extended system) is observable.
nO
is the dimension of the observable subspace of the extended system.
observabilityindices
is the list of observability indices for the extended system. The Inverse[
transformation
] will bring the system back to the original system together with extended states. The extended system in strict observer canonical form is output as
systeminobservercanonicalform
. (This command does not guarantee that the extended system admit uniform observability indices.)
​
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}=
strictOCFAD
[system]
State transformation is xold = transformation.xnew
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
 
▪
uniformobservabilityindices
 
▪
strictobservercanonicalform
 
▪
observabilityQandindices
RelatedGuides
▪
Guide for ZigangPan`LinearSystems`
""

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