《现代控制理论》刘豹著(第3版)课后习题答案

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38rankM23,I'8I=ᣚ'᪗"#஺01C0113NCA2CA179rankN3,%8KL=ᣚ%᪗"#஺3-11M1ᑡᢥ'ឋPQᑖS1210,b0,C111010(1)A0431S:Mb014rankM=2<3,I;Wᐰ'Ḅ஺AbA2b000913010,RAb0,R1,ᐸ];^_Ḅ8`⌕bc0᪀⌼᜻Y=ᣚ▣Rc-R1bR323130Rcbg஺010301hR1100001ᓽRcc1300100321Rlb0RclARc142cRc121c10003-12M1ᑡᢥ%ឋPQj᪀ᑖS1210,b0,C111010(1)04311210,b0,C111010S-ᵫhA0431C111232ᑣᨵNCA2CA474rankN=2<3,nI%111232᪀⌼o᜻Y=ᣚp▣RO1,ᨵRO1001311210qijR00010101x2uROlAROxROIbu2307321

39ycROx100x3-13M1ᑡᢥ'ឋ$%ឋPQj᪀ᑖS1001,b2,C112223(1)A2012S-ᵫhMAAb11121226Ab2202rankM=3,ᑣ'c1IcAN2cA71242511rankN=3,ᑣ%ᡠLv'wx%17111344yTc221226,ᑣT1c2713202231544002ᑣ1051,BT1c2b0cTc271301403-141ᑡ⌴ᦪ▣Ḅᨬ{|}஺(1)ws111s111S:1,B1110

400011Ac01B10,1100c01Cc11De00'I%yR11111001,qIJRO01ᡠLNR1OARO10,01KR1OBc1101CTCR10,DA00cOlO00ᡠLᨬ{|}Aஹ1,ITmii,rimA01,Dm0-CmsiA'mIB^m111s111w23003T51$2;'x%Ḅ1001-A1,b11,Cl2134

412-A22,b21,C21(1)ᑖ᪆ᵫ1$2ᡠᡂḄὶḄ'ឋ$%ឋ8wᑏᐸ⌴ᦪ;(2)ᑖ᪆ᵫ1$2ᡠᡂḄwὶḄ'ឋ$%ឋ8wᑏᐸ⌴ᦪ஺S-(1)1$2ὶ1Ḅyl;2Ḅᐭu2-8x32x32x1x20010x1u,340y001x2120MbAb0141413A2b014ᑣrankM=2<3,ᡠLIWᐰ'஺W(s)C(slA)IBs212(s2)(s3)(s4)s7s122hy2;1Ḅᐭul0x30140100u,y210x1x2112164MbAb00A2b1rankM=3ᑣ'c210321cAN2cA654rankN=2<3ᑣI%W(s)C(slA)IB1s27s12(2)1$2wὶ0010x1u,340y211x0021MAAb0141413Ab2124

42rankM=3,ᡠLWᐰ'c211322NcA24cA65rankN=3,ᡠLWᐰ%2s2s21wsCV2siABsIs2sK,ij.f-9c3-lb.-n-----fM4
IJ,1Z'ট(ᧇᐭ¢£K¤/஻§¨©ª«,¬“-®§jjf)32°3.±&³xᢗµ᪛5·ᐰ¸µᑜº.¼½¾¿ÀᵯÂᔲ,K.Ḇ,6*“W(s)=*3-----------J/S-#-ÄÄᡠ4)3aWমÆÇÈᒹ᫜ËÌ"Î1ÏД•Hr3ᡠLÓ]ÔÕÖ×Õ'ஹ%ឋØÙ஺ÚÛÜÝ⚪ßᫀ4-1ᑨá1ᑡâã#ᦪḄäåឋæ-22(1)Q(x)xl23x211x32x1x2x2x32x1x322(2)v(x)xl24x2x32x1x26x2x32x1x3S-(1)ᵫh

43Q(x)xlx2x31xl3x2x32xl1xlx211x3x22x3xlx211x3131121xl1x22x311113110,21120,311311710241

44vQ(x);é0Ḅ(2)ᵫh1112xlQ(x)xlx2x3xl4x23x3xl3x2x3x2x311lx1xxlx2x31432131x31111110,230,314316014131vQ(x)I;ê0Ḅ4-2Liâ▤Ḅ3᝱7-allal2xxaa2122í0ᙠï⊝3᝱ᜐᜧôõPö0Ḅᩩø஺S-ù(1)-⌕úᙠï⊝3᝱ᜐᜧôõPö08ᑣ⌕bcAḄᱯüýᙳᐹᨵ
஺IAᓽalla21al2a222(alla22)alla22al2a210ᨵᐹᨵ
஺ᓽalla220alla22al2a21(2)Ḅ⊝᝱xe0"ᜧ%&'()*+,ATPPAQ஺P0QI,2P11P12P12,ᑣ4ᐭATPPAQ,6ᑮP222alla12

4502a21alla222al20P111P0a21122a22P2212all2a21alla222al20a214(alla22)(alla22al2a21)0,ᑣ89:ᨵ;<஺ᓽ2a2222Aa21a22(al2a22a21all)IP22Aallal22(alla22)A(al2a22a21all)=al20ᐸ?detAAalla22al2a21⌕APB)ᑣ⌕A22Aa21a221Pll2(alla22)A0(alla22)2(al2a21)22P04(alla22)C8alla220,detA04-3DᵨlyapunovFGH)IᑡḄ()ឋ஺11(1)xx2311(2)xx112(1);<Ḅ⊝᝱Lxe0஺⌱0LyapunovNᦪ"V(x)xl2x20,ᑣV(x)2x1x12x2x22x1(xl2x2)2x2(2x13x2)22x126x1x26x23322(x1x2)2x2022V(x)L
)Ḅ஺x,ᨵV(x)஺ᓽᙠᜐᜧ%&'()஺2(2);<Ḅ⊝᝱Lxe0஺⌱0LyapunovNᦪ"V(x)xl2x20,ᑣV(x)2x1x12x2x2

462x1(xlx2)2x2(xlx2)22x122x20V(x)L
)Ḅ஺x,ᨵV(x)oᓽᙠᜐᜧ%&'()஺4-6WXYឋ᝱9"xlx2x2a(lx2)x2xl,a0DH)⊝᝱Ḅ()ឋ஺=Zᵨ[\]^_`ᑣa⚪cᨵ2x2f(x)2a(lx2)x2xl1f(x)OJ(x)1a4ax3ax2xT220PIQ(x)JT(x)J(x)1100221a4ax23ax21a4ax23ax200202a8ax26ax2ijkQ(x)ḄlmnH)ᦑᦋᵨqrst^FG஺⌱0LyapunovNᦪ"2V(x)xl2x20,{V(x)2x1x12x2x22x1x22x2(xla(lx2)2x2)222a(lx2)x20V(x)L
)Ḅ஺x4ᨵV(x)oᓽᙠᜐᜧ%&'()஺

474-7./130G=-3-2—3⊝᝱"|=[o0100-19/78-10/39-1/2ᵫ9GJFG-P=-I~P=-10/39-49/78-19/13,)m,C8&().0-1/2-19/13-121/26_▭Ḅᱯᐜ0.1173+2.6974i,0.1173.269741,-1.2346ᙠᓫ᜜.L9)Ḅ.“4-9WXYឋ9:xlx2x2xx2Dᵨ[\]^_`H)Ḅ()ឋ஺(1)Zᵨ[\]^_`a⚪cᨵ31x2f(x)3xx12J(x)f(x)02Tx3x1T11x22xx23x2(xl3x2)2xlx231V(x)f(x)f(x)x2x,ᨵV(x)o0PIQ(x)JT(x)J(x)03x1202113x1013x12213x21110ᑣQ(x)213x113x12᪷_ᱯᑨᨵ23x1212(3x121)0,Q(x)Ḅlmnᑨ஺23432x1x20,{IJ42010,213x12(2)qrst^⌱0LyapunovNᦪ"V(x)V(x)3x13x13x2x23x13x23x2(xl3x2)

4823x20V(x)L
)Ḅ஺xᨵV(x)oᓽᙠᜐᜧ%&'()஺4-lrtḄ⊝᪗Ji.ᵫ,%>0,q9st^Nᦪ"প=a/¢+¤r(x)=2axX+2¦¦=2al§~<2¦(஺ᑁᓝ~ª¦)=<20«¬¢<0>(ᵫ,~>஺>XB)஺]ll®¯=0°,x—>0¯=஺°.Xj—>0.ᓽ´µ¶r=[0¸7w°ᡈrG½Iᔙ¿02ᡝ")Âឤ"ÄᡠÆᙶ᪗L&()Ḅ¢ᵫ,IH-B,/(Qf8,Lᜧ%&()஺4-nᵨ[\]^_`,0p=134T:0]2||x||7oo,r(x)-8,C8¤⌕ᙠᙶ᪗&'()ᓺLᜧ%&()Ḅ¤⌕஺পு஺ᓺÔÕÖ'()ḄᩩØ.ÔÕ⌕AḄ஺ÙbḄ0%a<-lb<0.444T2DᵨÚÛÜÝ᪀⌼IᑡḄqrst^Nᦪxl-xl2x12x2x2-x2ᎷWV(x)ḄÜÝ"allxlal2x2VIVaxaxV2112222áâV(x)Ḅãᦪ":xl2x12x2al1x1al2x2a21xla22x222allxl2al2a21xlx2a22x22al2xl2x22allxl3x2T⌱äåᦪD⌱alla221,al2a210,,L6xlVIV2xx,ᓽ120,⊤jç⌱äḄåᦪLᐕéV,kᯠÔÕëÝ9x2xlx2xlx2Ḅ஺ᑣᨵ2V(x)(12xlx2)xl2x21112xx0ᡈxxxx᝞íᑣV(x)L
)ḄC812LxlÙx2ḄîïᩩØ஺121222

49áâ6ᑮV(x)":xl(x20)x2(xlxl)V(x)Oxldxl0x2dx212(xl2x2)2112xx0ᓽxxV(x)LB)ḄC8ᙠ%ᑁxe0L&()Ḅ஺12122Fðñò⚪óᫀ5-1õö᝱9"1110x0ux0111011DWá<᝱÷✄▣úûü᩽þÿT,-2,-3஺⚪ᨵ1110,b0A0111011MbAb011012rankMA2b3,஺1120(A,b,C)Ḅᱯ⚗IA(1)3(1)1332210100x0Uo001ᑣᑏᡂ᪗Iᑣᨵx1231ᐭ᝱!✄#Ḅ᝱$%x(AbK)xbu,ᐸ'K13(▣*Kk0klk2,ᑣK(A,bK,C)Ḅᱯ⚗f()det[I(AbK)]3(3k2)2(2kl)(1kO)᪷,-.Ḅ᩽012ᑮ45ᱯ⚗f*()(1)(2)(3)36211667f()9:()ᔜ=>⚗ᦪ@2k05kl9k29,ᑣᨵK5-9-9஺

5057ὊᨴᵨD⊈FᱥHᦈJKLMNOPQRSK=[£4A1TফV&(sl-"MX=ᵫ[\]Ὂஹ_--7,-3®f*«L(5l)(»)C+$)=5J65'ᓝ”S‘6JKttkᜐbc£23,4=-r஺£=-K12ு-a-7JA.4Me⁐Fᑗ[hijkl[m&᩽nᵯp"nKcir.K=".4Z.]*s)nqr-“<6ᑗ=/"஻-"(w”஻”£.”S4M.ᵫ[{f}~᣼R-2,7Q£%v=(spMCUjjMsFjfj,us'+'Os^^w^g6Kᐶ᡻5Q<=-4..᱐m᜛”=M4]£'1+£(5)J-6ᑗ=N+(3-Pஹ)5"”.-24£($>=(3+3)'=516s+71k*᱐4£=T,£=-3k=fn,-3j5-3ᨵ:210xx1uO1y10x

51(1)᪀஺(2)᝱ឋ]⌕¢@ᔲ¤¥¦᩽0§(3)ᢣ.᩽0-3,-3,¢᝱!✄▣஺(1)᪀᝞«:(2)¬ᵨ᝱!✄¤¥¦᩽0Ḅᐙ⌕ᩩ¯°0(A,b,C)µᐰ஺=·0(A,b,C)ᨵMb01rankM2,ᦑ᝱ឋ]⌕¢@Ab11¤¥¦᩽0஺(3)0(A,b,C)Ḅᱯ⚗IA(2)(1)232010ᑣᑏᡂ᪗Iᑣᨵxxu஺231ᐭ᝱!✄#Ḅ᝱$%x(AbK)xbu,*KkOkl,ᑣK(A,bK,C)Ḅᱯ⚗f()det[I(AbK)]2(3kl)(2kO)᪷,-.Ḅ᩽012ᑮ45ᱯ⚗f*()(3)226967f()9:()ᔜ=>⚗ᦪ@2kO7kl3,K73»5-4*Ï⌴Ñᦪ(s1)(s2)(s1)(s2)(s3)ÓÔᔲᑭᵨ᝱!✄Ï⌴ÑᦪÖᡂS1(s2)(s3)ᨵ@Ó¢᝱!✄K,×᪀஺(s1)(s2)s2s2W(s)(s1)(s2)(s3)s32s25s6ᵫ·Ï⌴ÑᦪÙÚ᩽0=ÛÜÝÞ஺

52᪗I0100x65y21000ulx211xßKk0klk2᝱!✄▣ᑣàáḄᱯ⚗f()det[I(AbK]3(2-k2)2(5-kl)(6kO)ᵫ·᝱!✄]ᦋÖḄÚ0᪷,⚪¥¦᩽0>-2,-2,-3,245ᱯ⚗f*()(2)(3)(2)372161267f()9:()Ḅ=>⚗ᦪ@2kO18kl21k25ᓽK18215᪀᝞«:⚪5-4᪀5-5äᑨæ«ᑡèé᝱!✄ᔲ╋.஺1222,b0011(1)A1011Ḅ▣

53MbAb240010rankMA2b3,஺115ᵫ.ᳮ5.2.1@ì¬ᵨ᝱!✄=0(A,b,C)¤¥¦᩽0Ḅᐙ⌕ᩩ¯°0(A,b,C)µᐰ஺íᵫ·rankM3,0(A,b,C)@c¬ᵨ᝱!✄Ḅ᩽0¥¦ᙠ᪷ï☢ḄTñäàá╋.஺’67eó*7"/ôj(s'-1))s#7.ö÷ᩩøùúûὡ⇵Q.',».qBu£®J4=oC6•fojxC"B"oj%=1:]]⍒74H&,5-7!"#$✄⊡'ᘤ)*+1sIW(s)1s(s1)1὚31὚4Ḅ᩽781,1,2,2஺1;W(s)W0(s)Wd(s)1s21sWd(s)W0(s)-lW(s)-l1Ws)-11ss20(11-11s(s1)-s(s1)(s2)s(s1)s11-1

54s(s2)ss2s2s-11-(s2)s(s2)s(sl)s1sIs1Wd(s)WO(s)IW(s)0s2s1s(s2)(s1)2(s2)sIs110(s2)2s2s(s1)2(s2)2(s2)s(sl)3(s1)(s2)5-10?@*+;x0100x01uy10x

55A!"#B᝱DEᘤ)DEᘤḄ᩽78-r,-2r(r>0)1;F8oNc10cA01GH*+IDJ᪀⌼DEᘤ஺*+ᱯNO⚗Q8detIAdet102,ᡠSᨵal0,a00,L01T1LN011001100110T0110UVT1TIbu001100uy0,1101WᐭY✄▣,)[DEᘤᱯNO⚗Q;2detI1det12221᪷]^_᩽7[^_ᱯNQ;f*r2r23r2r2`afbf*ᔜ⚗*ᦪ[;23r,12r22r2012r23rᓽYfᣚᑮXB᝱iG23r103r2rDEᘤjk8;

5612.l■nopqrst"uv᝞M)*ẑT4UN=T"ᱛ2[f]=[OI஺J7TLIOOJL|o6Jyz77":6=T2¸0L0IOoC=CT=[oo«j᳘=[;"}-["a2n[஺~7*N=[஺τ]ᑴy=&0*p8G=[]ÉI᝞ম=3",=5¸,S4ᡀ9:(5^4)(S-H)=s"+7S+”,“'/M1”-1"+["AGcx"buGyx3r22rl03ru2yx012r

57A5-13U5T2,!"ᶍ஺ytKOXsint,0t7-1(a)ytKOXsintKiaKOa,tytKXsint,t0ᐸarcsi22KOKIaaaarcsinNXKI1XXXaXXayt0,0ttযytKOXsint,yt0,tᐸarcsia

58a2K0aaNXKO1arcsin,Xa2XXX7-3K0.1ª«ᑴḄ*+¬ឋ®ᑖḄ᩽ᙶ᪗²³´¬ឋµ⁚Ḅ·᎔¹ᱯឋ᝞²A-7-1ᡠpGj2b1¼½7ᦑ*+¿À஺Á\vNX²A-7-1⚪7-3*+Ḅ¿Àឋᑖ᪆ÅGj=-180,JÆ[8.7,Ç8.7ÈᐭGj=1,J[K11.53,ÉK11.53ª*+yÊËÌÍᢝÏ₩஺40.117-4NX*+¬ឋ®ᑖḄ᩽ᙶ᪗²³´¬ឋµ⁚Ḅ·᎔¹ᱯឋ᝞²A-7-2ᡠÑXXᐸ21VÒÓÔÕᑮḄÖ¬஺2NX

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