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10
"I"L2=Jo
−r
∫
("I(t)"2
Rn)dt
W1,2([−r,o),Rn)
Notationsandsymbols
–isanorminL2([−r,o),Rn)
–isaspaceofallabsolutelycontinuousfunctions
withderivativesinaspace
ofLebesguesquareintegrablefunctions
oninterval[−r,o)withvaluesinRn
"I"W1,2=Jo
−r
∫
("I(t)"2
Rn+"
dI(t)
dt"2
Rn)dt–isanorminW1,2([−r,o),Rn)
PC([−r,o],Rn)
PC1([−r,o],Rn)
xt(to,I):[−h,o]→Rn
xt(I):[−h,o]→Rn
xt:[−h,o]→Rn
f(t+o)
f(t−o)
U(ξ)=
∫
o
Ż
KT(t)WK(t+ξ)dt
–isaspaceofallpiece-wisecontinuous
vectorvaluedfunctionsdefned
onthesegment[−r,o]
withtheuniformnorm
"I"PC=sup9∈[−r,o]"I(9)"
–isaspaceofallpiece-wisecontinuously
diferentiablevectorvaluedfunctionsdefned
onthesegment[−r,o]
withtheuniformnorm
"I"PC1=sup9∈[−r,o]"I(9)"
–isashiftedrestrictionofthefunctionx(·,to,I)
toaninterval[t−h,t]andisdefned
byaformulaxt(to,I)(9):=x(t+9,to,I)
fort≥toand9∈[−h,o]
–isashiftedrestrictionofthefunctionx(·,I)
toaninterval[t−h,t]andisdefned
byaformulaxt(I)(9):=x(t+9,I)
fort≥oand9∈[−h,o]
–isashiftedrestrictionofthefunctionx(·,I)
toaninterval[t−h,t]andisdefned
byaformulaxt(9):=x(t+9)
fort≥oand9∈[−h,o],
whenthefunctionIisknown
–istheright-hand-sidelimitoff(t)
atapointt,f(t+o)=limε→of(t+|ε|)
–istheleft-hand-sidelimitoff(t)
atapointt,f(t+o)=limε→of(t−|ε|)
–istheLyapunovmatrix
