《现代控制理论》第三版(刘豹.pdf

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4(ee)2(ee)1111SIA1142(S314(S30(t)1(t)S1S3S1111),2()S1S3S1),()eAt1 e3e4e3tet3tteAt0I1T2.xyx(0)01x00(1,0)x1,1.IAtt020u1u(t)A2t.2!1t01x xe x x0AteA(t)Bu()d1t01d01()d11 22tt222t21t1 =0111 t =1t0t0t127.1.u u(t)At23x0K K(t)x(0)Atx(t)e x0e BKBK,KxKxAtu u(t)t0e x x0e x x0AtAteA(t)BK K()d()d BK K0t0eA(t)e x x0eAtA(tAt)|BK Ke x x0e BK K2u u(t)xKxK1(1 t)e x x0e x x0e x x0e x x0AtAtAtAtt0 x x(0)eA(t)x x0BK K1(t)dd BK K)t0t0eA(t)A e11A(tAt|BK KI)BK KA(e3u u(t)Atk k1(t)t0 x x(0)et0A(t)x x0 x x(t)e x x0e x x0(eeAAtBK K 1(t)dd e BK KAteA)e|t0t0AA eAAt0t0AedAeAdt0eAdAAA11eteAA|t01t0eAAtAdt01A eA(e1|teAI)x x(t)e x x0AtA(e2AtI)A te11Ate BK KAte x x0AtA(e2AtI)A t BK K2-9.T0.1s2-21s,u1u21x1x2yx1x2y21x1Ku1x1u22x1x1x2x2K00u11u21010 x121x2IA1.101100;12IA P110P1100P1201TIA P2T01010111P2T101110TTP211G(T)eH(T)AT10TTT0eAtT01e1 ett0101T0e dtB0TTe1 e01K0dt011 eT1 eTTK00TK(1 e)TK(T1 e)x1(k1)x2(k1)eTTx1(k)G(T)x2(k)01x1(k)x2(k)0Tu1(k)H(T)u2(k)1 eK(1 eT)TK(T1 e)y(k)Tu1(k)u2(k)210.1se0.10.1x1(k)x2(k)010 x1(k)x2(k)u1(k)x1(k1)x2(k1)K(1 eK(e0.11 e)0.9).9)9)0.10.1u2(k)y(k)Tx1(k)21x2(k)1sx1(k1)x2(k1)K(1 e1)Ke1e01101x1(k)x2(k)1 eu1(k)1u2(k)y(k)21x1(k)x2(k)u1(k)TBu2(k)0Tu1(k)u2(k)x1(k1)x2(k1)1 TT01x1(k)(TAI)x2(k)x1(k)x2(k)0.900.110u1(k)0.1u2(k)KT0 x1(k)x2(k)T0.1sx1(k1)x2(k1)0.1K0T1s0011x1(k)x2(k)K00u1(k)1u2(k)x1(k1)x2(k1)12eAttABBA3-11x2ux4ya,b,c,dx1x2x3x4a0100b1000c1000dx1x2x3x410u00yx1x20010 x3x4b1000a010rankMa,b,c,dAbA b22MA ba02acccd33a02aca1a4,C001NCA11cCA2acbcc2CA3a2acc2b2bcc2c3rankN4,a,b,c,d2x1abx11x2cdx21uy10 x1x2MbAb1ba1cdM1ba1cdabcd0abcd0000NCCA10abb30abab31MMb Ab21 0cd 0 0cd31101121 01221NCCAN12022112MdetM1AbAb32T1324b13242411c10211431rankM0Ndet NCCA221CCA1102002343M123bAb21 323A b233222281433331 448223423132223detM1 42103142325103266224330NCCACA2W(s)03031400120114 det N41303s6s82s5122s4s3s4s3Ib01c5d201TTA1IIA1b4T52cd13M112bAbA b2001100201detM0rankM3Rc00101001000Rc130110120422detRc1000010TAbc3RcbcRc1RcARc1001111W(s)1s3ss2W(s)s113s100001s201102s000102000,010r0r0r101,100rIrI2r1000Ac0000000000Ir0rI1 rI10000010000010000010000000Bc0r0rIr00001000,0000011001100001Cc012:NCcCcAc2CcAc000001100000011100000000010100001000Rank(N)36Ro1000110000100001001000100100010000000001000000001100010010000001000011000Ro1RoAAAR11112oARoA21A220010001000000000000000000100011001001000BR101oBB1B2100000CCR1000oC1C201000000A11WAA11C1CB11001100,Bm0001000101000,01B1CmW(s)1s3ss13s012W(s)s101s100001102s002001,102000,011100000000000m0m0I000mA000oIm0m1I10m001000mIm2Im001000001000010B010110,21000C000010o0m0mIm000001:000000MBoAoBoA Bo2o000000010000010000100100100100001001rankM36Rc0001100110000000010000100010001000001Rc000100010000R1000001c0001100110001000000100000000AR110000cAoRc0000100000000001001BR100cBo000000000010CCoRc100100001000CB11010000,Bm1001000011001,00A11WAA11C1B1Cm123MA3-3bAbAbn 1n3234-11P11Q(x x)P12x x Px xP13P23P333231TP=P=P21P22P31P32202i11017.75020iQ(x x)10Q(x x)1111417.750T2P1x x Px x1312310Q(x x)3031604-2IA2a11a22a11a22a12a211122a11a2200a11a22a12a21P11P12P11P12P=P=A PPA Aa11a12a21a22P11P12TP12P222P12P22a11a21QIQP12P22a12a2210012(a11Pa21P11112)(a11a21)Pa21Pa21P2212112(a12Pa21P22)1120P11P22P12AA2aa222trA A22212a11a122trA Aa11a22a21a112trA AtrAAtrAa11a22AP11P11P22a11a22a12a21P0P12P21(AP11P22a2122PP12P21a11220a12)2)(Aa22)4trA A2(a12a222a21a11)224trA A2(a11a12)(a12a21)24trA AAP11a11a22a12a210A2000trA0a11a220a11a22a12a21a11a22004-31v(x x)0v(x x)P2v(x x)2x12x221x22xex x Px xT T06x26x1x2P1102330i361i0ii0Pv(x x)0 xTv(x x)A PPAQQIP745825838x21211020Pv(x x)2(xx222v(x x)xx2)0v(x x)120012x21A PPATQP4-21v(x x)x2x22x125-2M1b,Ab,A b321001001010010110990rankM2f()detIK(Abk)k03k1(11 10k2)k22(11 10k110k2)10k0f()(3*10)10)()(21j 3)(4 401.200.10101001j 3)12 2K224 44110110990Mb,Ab,A b32010rankM2IIA3112110011121110010001TcIA2bAbb21011010011121990100101110000.1000100T1cI00.100101000.10.1010A1cITcIATcI00101 1111bT1TcIb0012Kk0k1k2010AbK001k0k111k2110010111f()3(k211)*32(k111)2k0f()K12404Ab4113241314035-5KKTcM11.2A b00520.11b201detM0 RankMkM5-8(1)c1A Bc2A BdetE100010;c2A B10det10000c1A Bdetc2A B0;5-10(1)NccAIIIa11(2)deta0Txy(3):A0;LL;T12:;01;10L;0010g1g21u;0LN N1TATxT bubcTx01 xG,f()det2I(AGc)g11:g1g2g2(4)f*()(5)g12r;2r)(f()g2*2r)f()3r:G23r:2r22r3r2xGTG(7)x2r22r1 x03r22r:buGy(AGc)x1u03ry;22r xbuG(yAx01 x00(1)1u0)y3r(y22r);y(2)A-Gc=0100g1g2:1g110g2g1g210f()det I(A-Gc)=det2g1g2f()(G*r)(3r22r2r)23r2r25-12(1)I,rank c=1(2),001001T1c0c010,T0101001000010100AT1AT0100010100000100010001000101bT1b0100010010011000ccT001100010100 x3g1g2I(A11GA21)0010010g1g22001,y(3)G:f()detg1g2g201g1f()(5)g1(6)20;*4)(f()g295)f*()G2920:209(A11GA21)x1(A12GA22)y(B1GB2)uw011x20 x9Gyww10u;20y9(A11GA21)w(A11GA21)G(A12GA22)yw(B1GB2)u011x20w9Gyww180y61 120y91u;0 x1xx3Gy1wy100100w1w2209y1w120yw29yy(7)001010100w120yw29yyyw29yw120yxTx10