6.9.Excrciscs 123 with ~ + ( S ) =- c (6.50) ‘rhc component tiansfer finrictiori I122 ( ) i s ubtairicd by analysing the fewihack sjhteni t’ctilt consists of t,he loops ( f ) ;uid ~ ( t )with the notatioti F(s) = - I s G~s) A (6.51) we obtairi with (6.16) T is a unit) matrix, sizc N x N Now all c.oinpoi-rcnttxsnsfcr functiuns h a w been f o u i d WP obtain irorri (6.48) ;tnd ( 491, the cornplctc tiansfer finction is (6.53) o x will1 (6.47) (6.50) arid (6.52) (s) =G [SE - A]-’ (6.54) BY applying the I iiles tor conibinirig lirl-systems, we have foi.~rttlthe funclnmental connrction bet wecn the mitl-riccs of tlrc st a t e - s p x r model, and tlw tuinsfcr fiirictiori o C x system with rnult iplr inpints and outputs Exercise 6.1 Dcteriiiinc the transfer fnnction H (s) of the follo~ingseries resoriimt circuit iising coxnplrx irripcclnnccs L R R=l Exercise 6.2 Ihww thc fnnc(ioxi u ( f ) = ~ ( te ) f arid t h c tmgeiit at the i)oiiit,~ ( )The tangent caii i i h e ( l to help coiistrix*t thcl graph (if cxporrciiiia1 functions if its point of intcrsectivri with the z-axis i s ltriowri 1) mine [lie point of iiiterbectioit