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Hgv 'hf ³5hdghuv ,jqlwh /lwhudf\ ð 1 1 w y 1 1 1 1 ¢ 1 1 1 1. R á { x x L s v á x u y I O A J $ L O A J % L I O A J $ O A J % L t r I O A J u r O A J s r w L t r I r á w r á { x x L s r á u w s I $SOLFDQGR OD GHILQLFLyQ GH VHQR O A J v wº L s r á u w s L s r á u w s I O A J v wº L t r I r á y r y L s v á s v t I ð ñ Ñ Z ï ì Ñ A î ì u. We still have to satisfy the BC (4), u(x,L)=1, which gives (from (30)) 1= X∞ n=1 an sin nπx L sinh nπ (31) Eq(31) is a Fourier series We may obtain the values of the constants an by using the orthogonality of the eigenfunctions sin nπx L on the interval 0.

113 ñ ¾ ô ó ¨ ½ ¡  è û ¡ ñ ¢ à ç ¡ ¨ ÷ ¾ ì ÷ æ ó ÎÖÖÓ P ø Ⱥ ½/ ñ ¡ ù û ¢ ï ÎÓ ¹ Á m ¡ ÎÓÍ/ÒÎ ¢ ÿ Á ¡  ë. @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z \ ^ _ ` a b c d e f e g h i j k l m n o p q r s t u v w x y z {} ~ i j k l m n o. In control theory, a state observer or state estimator is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system It is typically computerimplemented, and provides the basis of many practical applications Knowing the system state is necessary to solve many control theory problems;.

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