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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`
DTRiccatiequation
​
X=DTRiccatiequation[a,s,q]
calculates the unique stabilizing solution to the discrete-time algebraic Riccati equation Transpose[
a
].Inverse[Inverse[
X
]+
s
]].
a
+
q
=
X
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 unit circle axis. The solution X is automatically positive semi-definite. The trivial case where all matrices
a
,
s
,
q
are {} is allowed, which results a solution
X
= {}.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
a={{-0.3,1},{0,-0.5}};b={{0},{1}};q=IdentityMatrix[2];​​
DTRiccatiequation
[a,b.Transpose[b],q]
Out[1]=
{{1.0956,-0.333669},{-0.333669,2.33731}}
SeeAlso
DTLyapunovequation
 
▪
Riccatiequation
 
▪
generalizedRiccatiequationHM
 
▪
linearLyapunovequation
""

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