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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`
generalizedRiccatiequationHM
​
z=generalizedRiccatiequationHM[a,s,q]
calculates the unique stabilizing solution to the generalized algebraic Riccati equation by finding the invariant subspace of the associated Hamiltonian. The solution
z
solves
Transpose
[a].z+z.a-z.s.z+
q
=0
where
a
,
s
, and
q
are square matrices,
s
and
q
are symmetric.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
a={{-1,1},{0,-1}};b={{0},{1}};d={{1},{0}};q=IdentityMatrix[2];γ=2;​​
generalizedRiccatiequationHM
[a,b.Transpose[b]-d.Transpose[d]/γ^2,q]
Out[1]=
{{0.510538,0.209967},{0.209967,0.559152}}
SeeAlso
linearLyapunovequation
 
▪
Riccatiequation
 
▪
DTLyapunovequation
 
▪
DTRiccatiequation
""

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