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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`
controllabilityQandindices
​
{systemcontrollable,nC,controllabilityindices,transformation}=controllabilityQandindices[a,b]
tests the controllability of the pair (a,b) and returns True if the pair is controllable in
systemcontrollable
.
nC
equals the dimension of the controllable subspace, and
controllabilityindices
is the list of controllability indices of the inputs, and
transformation
is an invertible matrix such that (Inverse[transformation].a.transformation,Inverse[transformation].b) is in controller canonical form. The trivial case where some or all dimensions of the matrices
a
,
b
are 0 are allowed.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
a={};b={};{systemcontrollable,nC,controllabilityindices,transformation}=
controllabilityQandindices
[a,b]
Zeroth order system!
Out[1]=
{True,0,{},{}}
In[2]:=
a={{2,1},{1,2}};b={{},{}};{systemcontrollable,nC,controllabilityindices,transformation}=
controllabilityQandindices
[a,b]
There is no input!
Out[2]=
{False,0,{},{{1,0},{0,1}}}
In[3]:=
a={{2,1},{1,2}};b={{1},{1}};{systemcontrollable,nC,controllabilityindices,transformation}=
controllabilityQandindices
[a,b]
Out[3]=
{False,1,{1},{{0,1},{1,-1}}}
SeeAlso
observabilityQandindices
 
▪
controllercanonicalform
 
▪
stablizabilityQ
RelatedGuides
▪
Guide for ZigangPan`LinearSystems`
""

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