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SmoothTransitionFunctions

Guides

  • Guide to ZigangPan`SmoothTransitionFunctions`

Symbols

  • Arztanfunction
  • flexibledeadzonefunction
  • mylegendPlot
  • SATF
  • simplesmoothfunction
  • smoothAsaturationfunction
  • smoothdeadzonefunction
  • smoothgrowthfunction
  • smoothsaturationfunction
  • smoothtransitionEfunction
  • smoothtransitionfunction
ZigangPan`SmoothTransitionFunctions`
Arztanfunction
​
Arztanfunction
[a,b]
is smooth on D = {(a, b) ∈ ^2 | a < 0 or b ≠ 0}. It is used in backstepping control design to eliminate unnecessary nonlinear term cancellation.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
Arztanfunction
[a,b]
Out[1]=
a+
2
a
-2/a

2
-1+
1
a


+
2
b
1-
-
1
2
b


b
b≠0&&a>0
a+
2
a
+
2
b
-
2
b
-
1
2
b

b
b≠0&&a≤0
0
True
In[2]:=
Plot3D
Arztanfunction
[a,b],{a,-2,2},{b,-2,2}
Out[2]=
SeeAlso
SATF
 
▪
smoothsaturationfunction
 
▪
smoothgrowthfunction
 
▪
simplesmoothfunction
 
▪
smoothtransitionfunction
 
▪
smoothtransitionEfunction
""

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