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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`
Riccatiequation
​
z=Riccatiequation[a,s,q]
​ calculates the unique stabilizing solution to the algebraic Riccati equation Transpose[
a
].
z
+
z
.
a
-
z
.
s
.
z
+
q
= 0 where
a
,
s
, and
q
are square matrices,
s
and
q
are positive semi-definite, the pair (a,s) is stabilizable, and the pair (a,q) admits no unobservable modes on the imaginary axis. The solution z is automatically positive semi-definite. The trivial case where all matrices
a
,s,q are {} is allowed, which results a solution
z
= {}.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
a={{-1,1},{0,-1}};b={{0},{1}};q=IdentityMatrix[2];​​
Riccatiequation
[a,b.Transpose[b],q]
Out[1]=
{{0.482028,0.189591},{0.189591,0.54246}}
SeeAlso
linearLyapunovequation
 
▪
generalizedRiccatiequationHM
 
▪
DTLyapunovequation
 
▪
DTRiccatiequation
""

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