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1 ode3a 3obusg ooag3ol gee 3y. Tee 1 osg 9o9ulf 3 solughba go gee H ooagol 93oblel 2 fo3 ulf ged 2a ge31 s of sgf ge s9f oe 1 fg32 que oy dol f 2a. To ff o2 2gf gege 2 dufl 3e 3eseagf gaba, gee follow lag aogf gaba fo3 f g f a sfe 3 fuaogaa of f sysgel bf sed oa 2gs sgf ge s9f oe 1 f g320es efs beea 2ag3o duoed (I)nt CI)I-An DC AlB 451) 4.2 Nominal Stability for Multivariable Systems Fa gee sequel, gee ooad 2Zbas fo3 ao1 aaf l sgf gab 2gy fo3 1 ulgaf 3f ble sysgel s wall be 9 3eseagec Teese ooad2g2ba s f3e eagaely f aflogous go geose fo3 scf If 3 (S So) sy sge l s. Jusg fs fo3 SeSO sysgel s, f l ugf 3/f ble sysgel 2 sgf ble, if fll 4s(S1 4e-MoMAlIf a )goles f 3e locf ged 2a gee fg ef If 9lf 4.2.1 Internal Stability Coa sade 3 gee ooag3ol sysgel 2 F2gu3e 4.2. Pa ooag f sg go 93ev 2ously, 2g 2 f ssul ed gef g fll gaf ls f 3e veco 3, f ad gef g fll gf a sfe fua ogpoas'f3e 1 fg32es of oo1 9fgzble d2l eas2oas noelke)nl). 2gu3e 4.2: Multivariable control system Agf a, 2age3afl sgf b 22gy wall be uade3sgood fs gee 9309e3gy, gef g f boua ded sagafl 2agoduoec f aywee3e 2a gee loo9 does aog sgal ulf ge f a uab ouaded s2gaf l f aywee 3e else 2a gee loo9. Jusg f s fo3 SRSO sysgel s, gee ooa agoa fo3 age afl sgf b21 2gy 3eduoes go sgf b 2gy of gee ool osage gf asfe3 1 fg f3o1 I)n(o3)n fad e I)ngo yI)n fad eI)n Hea oe, 2ageafl sgf b 212gy fo3 gee olosed loo9 sy gel 2 equ2vf leag go gee sysgel yI)n IIh(I)nkI)m (I)nkI)n IIh(I)nkI)m(I)n KI)nII h(I)nKI)m. -KI)nIIh(InKI)m(I)nEi)n efv2gfⅡ29oles2gee019 lex leng ef If 9lf ae.N08,ea8efo31的eM3eoe3名 gef a deal aaf go 3s 2(4.52), fs deaol af go3s do aog l fk 2(ve3y)21 903gf ag go 3el el be3 gef g 1 f g3% 1 ulg2912f g?oa 2 non-commutative, 2e. gef g gee ode 3 of gee ff ogo3s f 3e saga 2fiof ag fs i)nkint/ Kin( I)n 2 geae f I Fo3 gee sysge 1 2(4.52) go be sgf ble, fll fou3 g f a sfe3 1 f goes 1 usg be sgf ble Example 4.2(Internal st ability) If the controller ki)n is stable, internal stability can be checked by checking stability of the transfer function IIh( I)nKI)m (I)n Indeed, assume that KI)n and ITh( I)nKI)m (I)n￾                                                                                      ' ￾￾ ￾  ￾      "/#! ￾        ￾                                 ￾ !   @    ￾                &&!            ￾      ?      "( ￾                      = =           ￾ ￾ ￾ ￾ ￾ ￾￾ ￾ ￾      ￾ !￾ ￾ ￾ ￾ ￾  "(' ￾  ￾  ￾ 6                                        @    ￾                    %   ￾  ￾!  ￾  ￾  ￾ )                  ￾ ￾ ￾ ￾￾ ￾￾￾￾ ￾ ￾ ￾￾ ￾￾￾￾ ￾￾ ￾￾ ￾￾  ￾￾ ￾￾ ￾￾￾￾ ￾ ￾ "/(!         %        %             "/(!        +       &      !       %    ￾￾          $  ￾￾ ￾ ￾￾￾        "/(!                 # '   ) ￾   ￾   ￾  ￾% ￾ ￾￾       # ￾￾  ￾  ￾ ￾ ￾ ￾￾ ￾￾￾￾ )%  ￾ ￾ ￾  ￾ ￾￾ ￾￾￾￾ ￾ 
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