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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`
linearLyapunovequation
​
z=linearLyapunovequation[a,
b
,
c]
calculates the solution to the Lyapunov equation
z
.
a
+
b
.
z
=
c
assuming there exists a unique solution.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
a={{-1}};b={{-2,1},{-1,-1}};c={{1},{0}};
linearLyapunovequation
[a,b,c]
Out[1]=
-
2
7
,
1
7

In[2]:=
a={{-1,1},{0,-1}};b=Transpose[a];c=-{{1,0},{0,1}};
linearLyapunovequation
[a,b,c]
Out[2]=

1
2
,
1
4
,
1
4
,
3
4

SeeAlso
Riccatiequation
 
▪
generalizedRiccatiequationHM
 
▪
DTLyapunovequation
 
▪
DTRiccatiequation
""

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