第三章 線性控制系統(tǒng)能控性和能觀性

1、BuAxx0)(ftx)()() 1(kkkHuGxx),(BABn00321 (3-2)(3-1)b bu ux xx xb bu uJ Jx xx xnmmmmJ000010001100111111Tnbbbb21xccyubxx21221;000 xccyubxx21211;001xccyubxx21111;001111xxubxx22222x 1x xccyubxx21221;000)(0)(2txtx2111xxxubxx2212xccyubxx21211;001ubxxx12111212xxxccyubxx21111;001tiiex)0(BuAxxBuTzz1BuTJzz1tii

2、ex)0(tieubbxxxxxx323213113210000001. 121543214411154321210003001001101. 2uuxxxxxxxxxx213231121132131132100000001. 3uubbbbxxxxxxubbbbxxxxxxxxxx001101. 44321543214411154321u150154xx 0) 1)(5(541542AI1; 521111521ppT656161611T0115656161611bTuzbuTATzTz01100511uaaa100100010210 xx 232221321111T1231233131121

3、223231)()()(11TTTadj1231233131121223231)()()(1bTuTzz123123321100000011)(1;211013123112312131TT11)(1312311bT100;120100111211TT1001bTbuAxx12bAbAAbbMn000,)()()()()(0ttdtttttttbuxxdttttfttff)()()()(000buxdttftt)()()(000bux10njjjkka AA0!1)(kkkttketAA01001010)(!)(knjjjkjkknjjnjjjkktktaakttAAA0!)(kkjkjktat

4、dtfttjj)()(00u110120)(nntbAbAAbbxdttftt)()()(000bux101000)()()(0njjjnjttjjdttfbAubAx)()()(00201112110txtxtxnnnbAbAAbb12bAbAAbbMnuaaa100100010210 xx 221222110100aaaabAAbb22122110100aaaaM51255AbbMu150154xx bAIW1)()( ssux) 1() 1(5) 1)(5(115154)()(11ssssssssuxbAIWu150154xx 2012231210111001001)(ssasasasa

5、saasssWuxuaaa100100010210 xx BuAxx12BABAABBMnttjjdut0)()(01210120)(nntBABAABBx )(0trankrankxMM 1210120)(nntBABAABBx21001001301010121uuxx 011021001001301010121AB2410420110213010101212BA240100101010422101M2121723617626TMM010010102101ABBCxxAxxyxt00)(;)()(1ttyCxttdttttt0)()()()()(00BuxxCxyxxAxx00)(;tn00

6、21Amnmmnnccccccccc212222111211Cnnnxxxxxx2221110201021)(ntttxexexetnxnmnmmmnnnnxcxcxcyxcxcxcyxcxcxcy22112222121212121111202xet0201021222211121121)(ntttmnmmnnxexexeccccccccctyn333231232221131211cccccccccC3030203022010321111111! 21)()()()(xextexexetxtexetxtxtxtxtttttt111001001JA303020302201033323123222

7、1131211321111111! 21)()()()(xextexexetxtexeccccccccctytytyttttttty00)()(xxttt1000)()(njjjttttA000)(!1)(kkjkjttkatt1000)()()(njjjttttxCACxy01110)(xCACACIIIynnt1nCACACNTnTTTTTCACACN1)()()() 1(kkkhuGxx101,011220001hG)0(102122)0(101012011220001)0()0() 1 (, 0uuukhGxx) 1 (101)0(121062) 1 (101)0(1010112200

8、01122011220001) 1 ()0()0() 1 () 1 ()2(, 12uuuuuuukhGhxGhGxx)2(101) 1 (121)0(3214122)2(101) 1 (101011220001)0(121011220001062011220001)2() 1 ()0()0()2()2()3(, 223uuuuuuuuuxukhGhhGGhGxx4122)2() 1 ()0(113022111uuu11302211181154122113022111)2() 1 ()0(1uuu2hGhhG2hGGhhM 101)()0()(kjjkkjkhuGxGx)0()(101xGhu

9、Gnnjjnj)0() 1()2(.) 1 ()0(21xGhGhhGhGnnnnunuuu)0() 1()2() 1 ()0(21xGhGhhGhGnnnnunuuu)0()(101xGhuGnnjjnjhGhGGhhM12nn)()()(100010001)(100010121) 1(321kukukukkxx100010001H301010121GH10240104422HG1024301100010010010442121001M)0()0()0(301010121)2()2()2() 1 () 1 () 1 ()0()0()0(1003011024010010010001121442

10、3213321321321xxxuuuuuuuuu)0() 1()2() 1 ()0(21xGhGhhGhGnnnnunuuu)0()0()0(301010121)0()0()0(100010001321321xxxuuu)0()0(GxHu)()()() 1(kkkkCxyGxx)0()()0()(xCGyxGxkkkk)0() 1()0() 1 ()0()0(1xCGCGxCxnnyyy)0()0()0() 1() 1 ()0(211nnxxxnyyyCGCGCTTnTTTTCGCGCN)(11nCGCGCN11111111xCyuBxAx22222222xCyuBxAxTTT121212

11、,BCCBAA11111111xCyuBxAx22222222xCyuBxAxTTTTTTssss1111111121222)()()()(CAIBCAIBBAICW)()()(111112sssTWBAICW11111)()(BAICWss21AIAIss112AIAIAIsssT2122222BABABMnTTnTTTT11111112)(NCACACM1111112122222)(BABABCACACNnTnTTTTTTTT121212,BCCBAACxBuAxxynrankn1BAABB1101121321211nnnncbbAbATxTx1ccxybAxxu1210111100000

12、000010nnccATTA100011bTbc1101nccTcxcybxAxu01111nnnAIcbbAbcbbAbAc11212110)()(nnnnnnbbAbbbAbAbbAbAbAnnnnnnnnnnneeee11221221322111nceee211T111ccATTA212111nncceeeeeeAAAAATATnnnnnnnnnnnee0000122111322111)()(bbbAbbAbAbAbbAbbAAAnnnnnnneee1111221123122)()(bbAbbAbAbbAbAAAnnnnnnnneee22221211)()(bbAbbAbAbAAnnnn

13、nneee1111)(bbAbAbA12102111110211100000000010)()(nnnnnnnnnceeeeeeeeeeeAAAATT100bbTb11cbbT1c100211nnceeeebT100b1101132211,nnnnnnnbbAbbbAbAbAccnceee211ccTcccbbAbcbbAAbAc1121322110)(nnnnnnnnb10111121nnnnbbAbAcc101111211nnnncbbAbATc ,b ,Ac ,b ,AAc01110122111)()(ssssssssnnnnnnnbAIcWxuxx100112020113021y122

14、186116422bAAbbM293AI29, 0012092100010100010210A123109010001121216824161001010012122bAbbAccxuxx123100092100010y2932)(32012230122ssssssssssWcxbAxxyuxbAAbbxTx12ncxcbxAxyu000112bTbc1210212100010001000nccATTAxcbxAxyu1102nccTc01111nnnAIbcAcAbcb1110nnbAAbbM1nbuTxATTubxAx12212cccxcTxc2cyxTx2cbAAbbT12ncIAAAA

15、012211nnnnnbIAAAbAAbAT)(01221122nnnnc121012100010001000nncbAAbbATA bAbAAbbAAbbAATnnc212121022100010001000nccTAT1210212100010001000nccATTAbcAcAbcbcTc12ncbbAAbbbTb12nc0001b110ncbTb12cb29, 0012010901200100100210A001b12212bcAcAbcbcuxx001010901200 x1221ynrankTTnTTTTcAcAc1)(cxbAxxyuxTx01xcbxAxyu1210011010

16、00001000010nATTA110101nbTb000101 cTc1101ncAcAcNTTTTbccbAA*cbA,cbA,cbA,TTTbcccbbAAAcxbAxxyuxTx02ccAcAcAT211231211021000100101nnnnxcbxAxyu110102nTbb100002 cTc121002102100010001000naaaaATTAAb0111012211)(sssssssnnnnnnnW2260201002cAcAcN29, 0012092100010100010210A1221101bcAcAcbTb2001cuxx1221092100010 x001

17、y100;123;010901200cbAxuxx100123010901200yCxBuAxxy1BAABBMnnnrank1MxRxcxCyuBxAx1121nnnxxx11)(2212111011nnnnnnccAAAARRA11110nnncBBRB1121nnncCCCRC2222xAx uBxAxAx121211112 x2 xnnRRRRRc121xuxx210011310301100ynrank22103111012MbAAbbM110011001100110011321cRRAbRbR即xxcRxxbRxARRx21100110022111001111001100111001

18、10013103011001100110011111ccccyuuu110011101cRxuxx211001100221010yuxx01211011CxBuAxxy1nCACACNnnrank1N 0 xRx xCuBxAxy11222111010011nnnnnnAAAARRA112110nnnBBBRB11010nnnCCRCuBxAxAx222212121111111xCuBxAxynnRRRRR12110121,nRRRnnRR1110Rxuxx210011310301100y4323212102cAcAcNnrank 2N10R2101cR3212cAR1003R10020111

19、2,100321210010RR3R10RxxcRuxbuRxARRx001011101021010010010yCxyBuAxxxRx xCyuBxAx44433324232221131110000000AAAAAAAAAARRA00211BBBRB0031CCCRCCBA,ocococcoxxxx,ocococcoocococcoocococcoyxxxxCCuBBxxxxAAAAAAAAAxxxx000000000003121444333242322211311 )()()(111111BAICBAICWssscccxxRxcccRxxccccccccccccccyxxCCxxCRuBx

20、xAAABuRxxARRxx214211100cxococcxxRx02ocxocx02R), 0,(24CAc), 0,(24CAcococococococococococyxxCxxRCxxAAAxxRARxx0030222444333024102), 0,(24CAc),(11CA BcoccocxxRx01uBxAxAxccc21uBxxRAxxRAxxRocococcoocco02201101101RoccooccoocococcoocococcooccoyuxxCxxRCBBxxAAAxxAAAuBRxxRARxxRARxx00010121242313222111101022101

21、011101coxocx01R),(11CBAcocococcoocococcoocococcoyxxxxCCuBBxxxxAAAAAAAAAxxxx000000000003121444333242322211311xuxx210011310301100y110011101cRccccccyxxuxxxx211001100221110cxccccyxuxxx11012121101101110Roccooccococcooccoyxxxxuxxxxx011011110121110111uxxxxx0110112110111011211010111coccooccoococcoococcoococ

22、coyxxxuxxxxxx2010011002111016543212121654321654321002041005013006100347531101130134014xxxxxxyyuuxxxxxxxxxxxx645321xxxxxxocococcoxxxx6543212121654321654321002041005013006100347531101130134014xxxxxxyyuuxxxxxxxxxxxxocococcoocococcoocococcoxxxxyyuuxxxxxxxx020041050013000061347531100000030000101000010300

23、0000400000142121 ssWDBAIC1BuAxxDuCxy rkmisWik, 2 , 1;, 2 , 1 ssWD lim DWBAICss1 0111012211sssssssnnnnnnnWrnrrrrrrrrrrrrrrrcIIIII0000I0000I0A12101210ncCrrrrcBI000mnmmmmmmmmmmmmmmmII00I0I0I00II000A1210012100nBmmmI00C0 2113112ssssssssW 1101211131111ssssssDBAICW6,11, 62101111,4535,3626210362645351111611

24、61)34()65(23656116121113111223222223ssssssssssssssssssss60110600601106100000010000001000000100210rrrrrrrrrcIIII000I0A100100000000rrrcI00B114536113526210cC1101D601000060100110001001100016000000600002100mmmmmmmmmII0I0II00A1111453536262100B1000000100000mmmI00CCxyBuAxx xCyuBxAxxCxyBuAxx111,CBA 321211sssssW 1311321113321132113213ssssssssssssssssssW6,11, 621000,11,1321061011016002100mmmmmmmmmII0I0II00A0011132100B1000mmmI00C53110011111311660013020000BABABMnrank3M 2113112ssssssssW601106006011061000000