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AdvancesinAppliedMathematicsA^êÆ?Ð,2023,12(6),2643-2649
PublishedOnlineJune2023inHans.https://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2023.126266
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ANovelHybridSystem
JinfeiWei
SchoolofMathematicalSciences,ZhejiangNormalUniversity, Jinhua Zhejiang
Received:May5
th
,2023;accepted:May28
th
,2023;published:Jun.6
th
,2023
Abstract
Impulsivesystems,asatypeofhybridsystem,canbecombinedwithlogicaldynamic
systemstostudysystemswith logicselectiveimpulsiveeffects.Duetothefactthat the
powersystemconsistsofimpulsiveeffectsandlogicaloperations,theyaremoregeneral
andcomplexhybridsystems.Byusingthesemi-tensorproductmethodofmatrices,
©ÙÚ^:Ÿ7œ.˜«#.·ÜXÚ[J].A^êÆ?Ð,2023,12(6):2643-2649.
DOI:10.12677/aam.2023.126266
Ÿ7œ
the logicalfunction istransformedinto an equivalent algebraicform, making thestudy
ofsuchimpulsivesystemspossible.Thisarticlemainlyusesthesemitensorproduct
methodofmatricestocombineimpulsivesystemswithlogicaldynamicsystems.
Keywords
ImpulsiveSystem,LogicalDynamicSystem,TheSemiTensorProductofMatrices,
Stability
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/aam.2023.1262662644A^êÆ?Ð
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DOI:10.12677/aam.2023.1262662645A^êÆ?Ð
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h
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k
)).
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DOI:10.12677/aam.2023.1262662646A^êÆ?Ð
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2
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p
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p−1
Y
s=0
W
[n
p−s
m
p−s
,n]
ξ
p
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−
k
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1
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W
[N
2
n,m]
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h
L
g
M
[r,m]
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p
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g
W
[N
2
n
p
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DG(0)L
h
L
g
M
[r,m]
D
p−1
[m,m]
(
p−1
Y
s=0
W
[n
p−s
m
p−s
,n]
).(10)
Γ(ξ(t
−
k
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∞
X
p=1
1
p!
Γ
p
ξ
p
(t
−
k
).(11)
Ïd,XÚ(1)Œ±=†¤±e#XÚµ
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,
x(t) = D
η(t)
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−
),t= t
k
,k∈Z
+
,
x(0) = x
0
,
(12)
DOI:10.12677/aam.2023.1262662647A^êÆ?Ð
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η(t)
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k
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k
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0
x(t
−
k
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ë•©z
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Ÿ7œ
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DOI:10.12677/aam.2023.1262662649A^êÆ?Ð

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