Control en el espacio de estado CONSULTORES EDITORIALES Prof. Dr. PEDRO ALBERTOS PÉREZ Catedrático de Ingeniería de Sistemas y Automática UNIVERSIDAD POLITÉCNICA DE VALENCIA Prof. Dr. JAVIER ARACIL SANTONJA Catedrático de Ingeniería de Sistemas y Automática UNIVERSIDAD DE SEVILLA Prof. Dr. SEBASTIÁN DORMIDO BENCOMO Catedrático de Ingeniería de Sistemas y Automática UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA Control en el espacio de estado Segunda edición Sergio Domínguez Pascual Campoy José María Sebastián Agustín Jiménez Departamento de Automática, Ingeniería Electrónica e Informática Industrial Escuela Técnica Superior de Ingenieros Industriales Universidad Politécnica de Madrid Madrid ● México ● Santa Fe de Bogotá ● Buenos Aires ● Caracas ● Lima ● Montevideo ● San Juan ● San José ● Santiago ● Sao Paulo ● White Plains datos de catalogación bibliográfica CONTROL EN EL ESPACIO DE ESTADO Domínguez, S.; Campoy, P.; Sebastián, J.M.; Jiménez, A. Pearson Educación S.A., Madrid, 2006 ISBN 10: 84-8322-297-3 ISBN 13: 978-84-8322-297-3 Materia: Ingeniería de Control Automático, 681.5 Formato: 170 x 240 mm. Páginas: 440 Queda prohibida, salvo excepción prevista en la Ley, cualquier forma de reproducción, distribución, comunicación pública y transformación de esta obra sin contar con autorización de los titulares de propiedad intelectual. La infracción de los derechos mencionados puede ser constitutiva de delito contra la propiedad intelectual (arts. 270 y sgts. Código Penal). DERECHOS RESERVADOS 2006 por PEARSON EDUCACIÓN S.A.. Ribera del Loira, 28 28042 Madrid CONTROL EN EL ESPACIO DE ESTADO Domínguez, S.; Campoy, P.; Sebastián, J.M.; Jiménez, A. ISBN 10: 84-8322-297-3 ISBN 13: 978-84-8322-297-3 Deposito Legal: PRENTICE HALL es un sello editorial autorizado de PEARSON EDUCACIÓN S.A. Equipo editorial Editor: Miguel Martín-Romo Técnico editorial: Marta Caicoya Equipo de producción: Director: José A. Clares Técnico: María Alvear Diseño de cubierta: Equipo de diseño de Pearson Educación S.A. Impreso por: IMPRESO EN ESPAÑA - PRINTED IN SPAIN Este libro ha sido impreso con papel y tintas ecológicos a !"#$%& '# ()*$"*+)# , -. / 1212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12>2 ?74:@A57 8@ @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12>212 E67A;@8C8@B 8@ FCB GC6;CHF@B 8@ @B5C87 2 2 2 2 2 2 2 12=2 J:9C:;74@B 8@F K 78@F7 8@ @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12= 212 M;B5@K CB 8;4NK ;:7B F;4@CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 12= 2>2 M;B5@K CB 8;4NK ;:7B ;4GC6;C45@B 2 2 2 2 2 2 2 2 2 2 2 12D 2 O6C4BP76K C:;74@B F;4@CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12Q2 R@A6@B@45C:;<4 S6NT:C 8@ B;B5@K CB F;4@CF@B 2 2 2 2 2 2 2 2 2 12U2 V94:;<4 8@ 56C4BP@6@4:;C W K 78@F7 8@ @B5C87 2 2 2 2 2 2 2 2 12I2 X Y5787B 8@ 7H5@4:;<4 8@F K 78@F7 8@ @B5C87 2 2 2 2 2 2 2 2 12I212 ZC6;CHF@B 8@ @B5C87 :7K 7 K CS4;598@B P[B;:CB 2 2 2 2 12I2>2 ZC6;CHF@B 8@ @B5C87 :7K 7 BCF;8C 8@ F7B ;45@S6C876@B 12I2= 2 ZC6;CHF@B 8@ @B5C87 8@ PCB@ 2 2 2 2 2 2 2 2 2 2 2 2 2 12I2D 2 ZC6;CHF@B 8@ ]768C4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12I2Q2 JB569:596CB :7K A9@B5CB 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12^2 J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12L2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ` 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 = D I L 1> 1= 1D 1Q 1I 1L >\ >> >I >^ =\ == DQ ` 121\2 J_@6:;:;7B A67A9@B57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U\ . >212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >2>2 M7F9:;<4 8@ FC @:9C:;<4 7K 7SY4@C 2 X C56; 8@ 56C4B;:;<4 >2>212 ?CB7 S@4@6CF 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >2>2>2 ?CB7B AC65;:9FC6@B 8@ FC K C56; 8@ 56C4B;:;<4 2 2 >2=2 E67A;@8C8@B 8@ FC K C56; 8@ 56C4B;:;<4 2 2 2 2 2 2 2 2 2 2 >2D 2 M7F9:;<4 8@ FC @:9C:;<4 :7K AF@5C 2 2 2 2 2 2 2 2 2 2 2 2 2 >2Q2 ?NF:9F7 8@ FC K C56; 8@ 56C4B;:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 >2Q212 X Y5787 8@ ?CWF@W CK ;F574 2 2 2 2 2 2 2 2 2 2 2 2 >2Q2>2 X Y5787 8@ ]768C4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >2Q2=2 X @8;C45@ FC 56C4BP76K C8C ;4G@6BC 8@ CAFC:@ 2 2 >2U2 J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >2I2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 U= UD UD UQ U^ I\ I> I> IQ I^ IL ^L =212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2>2 @T4;:;74@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2=2 ?74567FCH;F;8C8 @4 B;B5@K CB F;4@CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2=212 ?NF:9F7 8@ FC @456C8C @4 B;B5@K CB F;4@CF@B 2 2 2 2 2 2 =2D 2 ?74567FCH;F;8C8 @4 B;B5@K CB F;4@CF@B ;4GC6;C45@B 2 2 2 2 2 2 2 =2D 212 34GC6;C4 C 8@ FC :74567FCH;F;8C8 C45@ :CKH;7 8@ HCB@ =2Q2 4 345@6A6@5C:;<4 S@7K Y56;:C 8@ FC :74567FCH;F;8C8 2 2 2 2 2 2 =2U2 M9H@BAC:;7 :74567FCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2U212 CB@ 8@F B9H@BAC:;7 :74567FCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 =2U2>2 JB5C87B CF:C4 CHF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2I2 M@AC6C:;<4 8@F B9HB;B5@K C :74567FCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 =2^2 ?74567FCH;F;8C8 8@ FC BCF;8C 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2L2 J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =21\2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2112 J_@6:;:;7B A67A9@B57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1\L 11> 11= 11U 1>> 1>Q 1>Q 1>^ 1=\ 1=\ 1=1 1=D 1=I 1Q> 1I1 D 212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2>2 @T4;:;74@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2=2 HB@6GCH;F;8C8 @4 B;B5@K CB F;4@CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2=212 EFC45@CK ;@457 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2=2>2 O@76@K C 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2=2=2 @5@6K ;4C:;<4 8@F @B5C87 ;4;:;CF @4 B;B5@K CB 7HB@6GCHF@B D 2=2D 2 JB5C87B 47 7HB@6GCHF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2D 2 M;B5@K CB F;4@CF@B ;4GC6;C45@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2D 212 34GC6;C4 C 8@ FC 7HB@6GCH;F;8C8 C45@ :CKH;7 8@ HCB@ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1IQ 1II 1II 1II 1I^ 1^1 1^= 1^Q 1^I 0. . 2 2 2 2 2 2 2 2 2 2 2 2 ` D 2Q2 4 345@6A6@5C:;<4 S@7KY56;:C 8@ FC 7HB@6GCH;F;8C8 2 2 2 2 2 2 2 2 2 D 2U2 M9H@BAC:;7 47 7HB@6GCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2U 212 CB@ 8@F B9H@BAC:;7 47 7HB@6GCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2I2 M@AC6C:;<4 8@F B9HB;B5@K C 47 7HB@6GCHF@ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2^2 M@AC6C:;<4 8@ F7B B9HB;B5@K CB :74567FCHF@ W 7HB@6GCHF@ 2 2 2 2 2 2 D 2^ 212 ?NF:9F7 8@ FC K C56; 8@ :CKH;7 8@ HCB@ 2 2 2 2 2 2 2 2 2 2 D 2L2 4 R@89::;<4 8@F K 78@F7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2L 212 ZCF76@B B;4S9FC6@B 8@ C4 @F W 6@CF; C:;74@B @ 9;F;H6C8CB 2 D 2L 2>2 O6C4BP76K C:;<4 C FC 6@CF; C:;<4 ;45@64CK @45@ @ 9;F;H6C8C D 2L 2= 2 R@89::;<4 8@F K78@F7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 21\ 2 J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 D 2112 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1^^ 1^L 1L\ 1L 1 1LD 1LI 1L^ 1LL >\ 1 >\D >\L >1D 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 R@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ?74567F 8@ B;B5@K CB K747GC6;CHF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Q2= 212 ;B@ 7 8@F H9:F@ 8@ 6@CF;K @45C:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Q2= 2>2 H5@4:;<4 8@ FC K C56; 8@ 56C4BP76K C:;<4 C GC6;CHF@B 8@ PCB@ Q2= 2= 2 JF A67HF@K C 8@ FC SC4C4:;C 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Q2= 2D 2 ;B@ 7 8@ B@6G7B;B5@K CB 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ?74567F 8@ B;B5@K CB K9F5;GC6;CHF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 Q2D 212 ;B@ 7 8@F H9:F@ 8@ 6@CF;K @45C:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Q2D 2>2 H5@4:;<4 8@ FC K C56; 8@ 56C4BP76K C:;<4 C GC6;CHF@B 8@ PCB@ J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 J_@6:;:;7B A67A9@B57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0>= 1 >== >=D >=D >=^ >=L >D= >DL >DL >Q= >QQ >ID >^D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >^I >^^ >L 1 >L 1 >L= >LQ >LL =\\ =\Q =\^ =1> =>Q ==^ . Q212 Q2>2 Q2=2 2 2 2 2 2 2 2 2 2 2 2 2 Q2D 2 Q2Q2 Q2U2 Q2I2 . U212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U2>2 @T4;:;<4 8@ 7HB@6GC876@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U2=2 ?7KA765CK ;@457 8@F :74_9457 B;B5@K C 7HB@6GC876 2 2 U 2= 212 M;4 6@CF;K@45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 U 2= 2>2 ?74 6@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 U2D 2 ?NF:9F7 8@F 7HB@6GC876 @4 B;B5@K CB K 747GC6;CHF@B 2 2 U 2D 212 ?NF:9F7 8@ FC K C56; 8@ 56C4BP76K C:;<4 2 2 2 2 U2Q2 4 ?NF:9F7 8@F 7HB@6GC876 @4 B;B5@K CB K9F5;GC6;CHF@B U 2Q212 ?NF:9F7 8@ FC K C56; 8@ 56C4BP76K C:;<4 2 2 2 2 U2U2 HB@6GC876@B 8@ 768@4 6@89:;87 2 2 2 2 2 2 2 2 2 2 2 2 U2I2 J_@K AF7B C8;:;74CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U2^2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U2L2 J_@6:;:;7B A67A9@B57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ` !"#$%& '# "#( %$)# , . / I212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2>2 @T4;:;<4 8@ @B5C87 AC6C B;B5@K CB 8;B:6@57B 2 2 2 2 2 2 2 2 I2=2 M;B5@K CB 8;4NK;:7B 8;B:6@57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2D 2 H5@4:;<4 8@ K 78@F7B 8;B:6@57B 8@ @B5C87 2 2 2 2 2 2 2 2 2 I2D 212 X 78@F7 8@ @B5C87 @4 GC6;CHF@B 8@ PCB@ 2 2 2 2 2 2 2 I2D 2>2 X 78@F7 8@ @B5C87 @4 GC6;CHF@B 8@ ]768C4 2 2 2 2 2 2 I2D 2=2 O6C4BP76K C:;74@B F;4@CF@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2Q2 H5@4:;<4 8@ FC 6@A6@B@45C:;<4 @ 5@64C C AC65;6 8@F @B5C87 I2U2 M;B5@K CB K9@B56@C87B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2U212 M;B5@K C 8;B:6@57 ;4GC6;C45@ @ 9;GCF@45@ 2 2 2 2 2 2 2 I2U2>2 M;B5@K CB GC6;C45@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2U2=2 M;B5@K CB [H6;87B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 I2U2D 2 M;B5@K CB [H6;87B 6@CF;K @45C87B 2 2 2 2 2 2 2 2 2 2 2 I2I2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 =D= =DD =DD =DU =DI =D^ =Q\ =Q1 =Q> =Q> =QD =QQ =QU =QI ^212 3456789::;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ^2>2 M7F9:;<4 8@ FC @:9C:;<4 7K 7SY4@C 2 X C56; 8@ 56C4B;:;<4 ^2=2 E67A;@8C8@B 8@ FC K C56; 8@ 56C4B;:;<4 2 2 2 2 2 2 2 2 2 2 ^2D 2 ?NF:9F7 8@ FC K C56; 8@ 56C4B;:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 ^2D 212 X Y5787 ;5@6C5;G7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ^2D 2>2 X Y5787 8@ FC K C56; P948CK @45CF 8@ B7F9:;74@B 2 ^2D 2=2 X Y5787 8@ 8;CS74CF; C:;<4 8@ ]768C4 2 2 2 2 2 2 ^2D 2D 2 X Y5787 8@ ?CWF@W CK ;F574 2 2 2 2 2 2 2 2 2 2 2 2 ^2D 2Q2 X Y5787 8@ FC K C56; 6@B7FG@45@ 2 2 2 2 2 2 2 2 2 2 ^2Q2 M7F9:;<4 8@ FC @:9C:;<4 :7K AF@5C 2 2 2 2 2 2 2 2 2 2 2 2 2 ^2U2 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 =UQ =UQ =UU =UI =UI =U^ =I\ =I\ =I> =ID =IQ L212 ?74567FCH;F;8C8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 L2>2 ?74567FCH;F;8C8 @4 B;B5@K CB 8;B:6@57B F;4@CF@B 2 2 2 2 2 2 2 2 L2=2 ?74567FCH;F;8C8 @4 B;B5@K CB 8;B:6@57B F;4@CF@B ;4GC6;C45@B 2 2 L2D 2 ?74567FCH;F;8C8 8@ FC BCF;8C 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 L2Q2 HB@6GCH;F;8C8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 L2U2 HB@6GCH;F;8C8 @4 B;B5@K CB 8;B:6@57B F;4@CF@B 2 2 2 2 2 2 2 2 2 L2I2 HB@6GCH;F;8C8 @4 B;B5@K CB 8;B:6@57B F;4@CF@B ;4GC6;C45@B 2 2 L2^2 ?74567FCH;F;8C8 W 7HB@6GCH;F;8C8 @4 B;B5@K CB K9@B56@C87B 2 L2L2 ?74567F 8@ B;B5@K CB 8;B:6@57B A76 6@CF;K @45C:;<4 8@F @B5C87 L21\2 M;B5@K CB K9@B56@C87B 8@ :74567F 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 L2112 J_@6:;:;7B 6@B9@F57B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 =IL =^\ =^> =^D =^Q =^U =^^ =L\ =L> =L= =LI . . 2 2 2 2 2 2 2 2 2 2 2 * "(%# . 212 @T4;:;74@B 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2>2 ;CS74CF; C:;<4 8@ 94C K C56; @4 :C_CB 8@ ]768C4 2 2=2 ?NF:9F7 8@F G@:576 A67A;7 CB7:;C87 C 94 GCF76 A67A;7 2 2 2 2 2 2 2 2 2 2 2 2 D\Q 2 2 2 2 2 2 2 2 2 2 2 2 D\U 2 2 2 2 2 2 2 2 2 2 2 2 D\I - -0 1212 JG7F9:;<4 5@K A76CF 8@ FCB GC6;CHF@B 8@ @B5C87 2 2 2 2 2 2 2 12>2 O6CW@:576;C 8@F G@:576 8@ @B5C87 @4 @F @BAC:;7 8@ @B5C87 2 12=2 O6C4B;5;G;8C8 8@ @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12D 2 F7 9@ ;45@S6C8762 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12Q2 X 9F5;AF;:C:;<4 A76 94C K C56; 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12U2 F7 9@ B9K C8762 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12I2 R@A6@B@45C:;<4 S6NT:C 8@F K78@F7 8@ @B5C87 2 2 2 2 2 2 2 12^2 R@A6@B@45C:;<4 S6NT:C G@:576;CF 8@F K 78@F7 8@ @B5C87 2 2 12L2 M;B5@K CB @4 B@6;@2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 121\ 2 M;B5@K CB @4 AC6CF@F7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12112 R@CF;K @45C:;<4 :74B5C45@ 8@ FC BCF;8C 2 2 2 2 2 2 2 2 2 2 2 121>2 R@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ^ ^ L 1Q 1Q 1U 1I 1I =\ =1 => == =212 M;B5@K C 47 :74567FCHF@2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2>2 E9457B CF:C4 CHF@B 8@B8@ \ \ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =2=2 O6C4B;:;<4 8@F @B5C87 @456@ 87B A9457B 8@ P76K C 8;6@:5C F[4@C :745;49C W :74 94 A9457 8@ ACB7 ;45@6K @8;7 F[4@C 8;B:745;49C 2 2 2 2 2 2 2 2 2 2 2 =2D 2 M9A@6A7B;:;<4 8@ FC @G7F9:;<4 F;H6@ :74 @F B9H@BAC:;7 :74567FCHF@ 2 2 2 2 2 =2Q2 R@A6@B@45C:;<4 S6NT:C 8@F B9HB;B5@K C :74567FCHF@2 2 2 2 2 2 2 2 2 2 2 2 2 2 11\ 2 11\ D 212 D 2>2 D 2=2 D 2D 2 D 2Q2 ?74:@A57 8@ 7HB@6GCH;F;8C8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 M;B5@K C F;4@CF :74 @F :74_9457 8@ @456C8CB 8@ 5@B5 2 2 2 2 2 2 2 2 2 2 M@AC6C:;<4 8@ FC AC65@ 47 7HB@6GCHF@2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 M@AC6C:;<4 B;K9F5N4@C 8@ F7B B9HB;B5@K CB :74567FCHF@ W 7HB@6GCHF@ 2 M@AC6C:;<4 8@5CFFC8C 8@ F7B B9HB;B5@K CB :74567FCHF@ W 7HB@6GCHF@2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1IQ 1^^ 1L= 1LU 1LI Q212 Q2>2 Q2=2 Q2D 2 Q2Q2 M;B5@K C :74 6@CF;K @45C:;<4 8@ @B5C87 2 2 2 2 2 2 2 2 O6C4BP76K C:;<4 8@ FC K C56; 8@ 6@CF;K @45C:;<4 K 2 8;:;<4 8@F AC6NK @567 22 2 2 2 2 2 2 2 2 2 2 2 2 2 K0 R@CF;K @45C:;<4 @4 B;B5@K C 8@ 5;A7 947 2 2 2 2 2 2 2 ?74567F A67A76:;74CF 8@F B;B5@K C C45@6;762 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >== >D\ >D 1 >DD >DQ 2 11^ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1= 1 2 1== Q2U2 ?74G@6B;<4 C B;B5@K C 8@ 5;A7 947 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >DU U212 U2>2 U2=2 U2D 2 U2Q2 U2U2 U2I2 ?74:@A57 8@ 7HB@6GC8762 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 M;B5@K C :74 7HB@6GC876 W 6@CF;K @45C:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 JB 9@K C 8@F B;B5@K C :74 7HB@6GC8762 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 M;B5@K C :74 7HB@6GC876 W 6@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 2 2 2 2 JB 9@K C 8@B B;B5@K C :74 7HB@6GC876 @4 FC P76K C :C4<4;:C 7HB@6GCHF@ 2 2 2 M;B5@K C :74 7HB@6GC876 W K C56; 8@ 56C4BP76K C:;<4 2 2 2 2 2 2 2 2 2 2 2 2 2 JB 9@K C 8@B B;B5@K C :74 7HB@6GC876 W 6@CF;K @45C:;<4 @4 @BAC:;7 8@ @B5C87 56C4BP76K C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 U2^2 M;B5@K C :74 7HB@6GC876 8@ 768@4 6@89:;87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 >^I >^^ >L> >L= >LI =\\ I212 I2>2 I2=2 I2D 2 M;B5@K C M;B5@K C M;B5@K C M;B5@K C L212 L2>2 L2=2 L2D 2 L2Q2 L2U2 M;B5@K C M;B5@K C M;B5@K C M;B5@K C M;B5@K C M;B5@K C :745;497 K9F5;GC6;CHF@2 2 2 2 2 2 2 2 8;B:6@57 @ 9;GCF@45@2 2 2 2 2 2 2 2 2 :74 AC65@ 8;B:6@5C W AC65@ :745;49C2 [H6;87 6@CF;K@45C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =Q> =Q= =QQ =QI K9@B56@C87 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8;B:6@57 :74 6@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 2 2 K9@B56@C87 :74 6@CF;K @45C:;<4 8@F @B5C87 2 2 2 2 2 2 2 2 2 K9@B56@C87 :74 5;@K A7 8@ :NF:9F7 49F7 2 2 2 2 2 2 2 2 2 2 2 K9@B56@C87 :74 5;@K A7 8@ :NF:9F7 47 49F7 2 2 2 2 2 2 2 2 2 :74 6@5C687 47 K F5;AF7 @45@67 8@F 5;@K A7 8@ K9@B56@7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =L\ =L> =L= =LD =LQ =LU 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 =\1 =1\ J4 CA@4CB :;4:9@45C C 7B @F ?74567F 957K N5;:7 C ;669KA;87 :7K7 94C 8;B:;AF;4C A9_C45@ W 8@ S6C4 ;45@6YB 47 B<F7 :;@45[T:7 W 5@:47F<S;:7 B;47 5CKH;Y4 @:74<K ;:7 2 7B B;B5@K CB 8@ :74567F C957K N5;:7 9@ 5;@4@4 B9B 76[S@4@B @4 FC K NB 6@K75C C45;S @8C8 C4 B9B5@45C87 B9B 6C[:@B @4 FCB K C5@K N5;:CB CAF;:C8CB W B@ @B5N4 :74G;65;@487 8@ K C4@6C :C8C G@ K NB :6@:;@45@ @4 :7KA74@45@B @B@4:;CF@B W :6[5;:7B 8@ :9CF 9;@6 B;B5@K C 8;4NK ; 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