一类固定时刻脉冲微分系统变差稳定性-variation stability of a class of impulsive differential systems with fixed time.docxVIP
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一类固定时刻脉冲微分系统变差稳定性-variation stability of a class of impulsive differential systems with fixed time
?1=1脉?②???????突?②?,??⑧??②????????????,其数?????????脉????统.脉????统????不?脉?????统????????述???物??③??.????术????术????络????衡?⑤????工??????,脉????统?????????和????论??,?上????????,■??◆多???者都对其????研?????很??展[1?19].??????建立脉????统?▲??,?多????脉???,?统????[1?14].??研??不断??,???统??脉????????不?满?②????■?.⑦?对???度????数[20?32],??不连??,??????绝对连??,对?这???,?出②脉?后,??????研?就具?????论??.??这??度???数?⑩????论???对策???器◆???→??????,?40????,出②??量研????度???数??③[20?39].?Jordan引?????????数???,???????????????推?和??[40?44].1959?,H.Okamura?出????????,?I.Vrkoc??③[44]?研?Caratheodory?统,??出H.Okamura?????????????????;1998?,??????③[22]??合?????数?论,⑤?Henstock??和Schauder-Tichonov不????建立??????不连??统??????⑧??和???,其?????具???不连??,其??绝对连???????;?后,????又??③[23]?建立???不连??统???????????和渐????????;2000?,?⑧????[16]??论???脉????统???满?Caratheodory???,初?????⑧??;2001?,???和??▲??[17]??论????合?脉????统???和脉????均不连?,??满?Caratheodory??和脉????连??两????,脉????统??⑧??.?言??将?????[22]??论???不连??统???dxdt=f(t,x)0??x(t+)=x0推???脉???:?dx?dt=f(t,x),t/=ti??(I)?x=Ii(x),t=ti,i=1,2,···??(II)0?x(t+)=x0,i+其?(H1)0t1t2···ti···,?lim→∞ti=+∞;(H2)f:R+×B→Rn,?t∈R+,?f(t,0)=0,B?Rn????;(H3)Ii:B→Rn,Ii(0)=0,?Ii∈C(B,Rn),i∈N,N???数?,Rn?具?通⑦?数·?n?欧???.IVP(II)???脉???ti??连??,?x(t?)=x(ti),x(t+)=x(ti)+Ii(x(ti)),i=1,2,···.对③??数x(t):B→Rn,除ii??ti????连??.x(t,t0,x0)▲?IVP(II)▲初??x(t0,x0)??.?助不连??统(I)???????论和脉????统引论,???论IVP(II)??????⑧??和???,??出⑧??和????????.其?,???上述?论???上⑤??[31]对Kurzweil????????????析?⑤,?论IVP(II)???????????,?出??????和渐??????两?Lyapunov?????.⑩后,??对IVP(II)????⑦????g(t,x),??dx?dt=f(t,x)+g(t,x),t/=ti???x=Ii(x),t=ti,i=1,2,···?0??x(t+)=x0,(III)??论??统???????????,?出?????IVP(II)和???脉????统(III)????????和渐?????????.???????部??◆:??部?????????,???引?;??部??论??????脉????统??????⑧??和???;??部??出??脉????统???????????和渐???????Lyapunov???;??部??论??脉????统??⑦?????,???????????,?建立这?脉????统????和???????????和渐???????????.§1预?⑧??IVP(II)?⑩?脉??ti,i=0,1,···,k?1,k∈N???论.??⑩?脉??ti∈(a,b)?R+,?Bc={x∈Rn,IxIc},c0?⑦数,G=Bc×(a,b)?Rn+1????,?引??→??记号:Si=(t,x)∈R+×Rn:t=ti,i=0,1,···,k?1;kΘi=(t,x)∈R+×Rn:ti1t≤t,Θ=IΘ;?Θ0niii=1k0I0i=(t,x)∈R+×R:ti?1tti,Θ=
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