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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`
ZDCF
​
{
ZDCFQ,transformation,zerodynamics}=ZDCF[system]
calculates the zero dynamics canonical form for MIMO LTI system with well-defined vector relative degree. It requires the system to admit vector relative degree, and then calculates the state transformation that will bring the system into the zero dynamics canonical form, and the zero dynamics canonical form itself.
ZDCFQ
= True if the system admits vector relative degree, False otherwise;
transformation
= the state transformation xold = transformation.xnew that brings the system into zero-dynamics canonical form;
zerodynamics
= the zero-dynamics canonical form of the system, where the zero dynamics is the extended zero dynamics.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
system1={{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},{0,0,1,0,0,0,1},{1,0,0,0,0,0,0},{0,0,1,0,0,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}};
In[2]:=
ZDCF
[system1]
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
Out[2]=
True,{1,0,0},
1
2
,
1
2
,0,{0,0,1},{{x1,x2,x3},{u1,u2,w1,w2,y1,y2},{y1,y2,z1,z2},{{0,1,0,0,0,0,1,0,0},{-5,-2,2,2,2,2,-1,0,0},{-2,-1,-3,-1,1,1,1,0,0},{1,0,0,0,0,1,0,0,0},{0,0,1,0,0,0,1,0,0},{1,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4,5,6},{1,2},{3,4}}
SeeAlso
EZDCF
 
▪
EZDCFAD
""

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