12% Analysis of C'oiitinuous-Time LTI-Syst,ems with 11ie 1,aplate Transfom many lirl-systerris As RII example for rhcir systernatic use, IT e will calciilal e the transftJr fuirction of' a general slate-space repieseiitiitioii foi it systcrn with miiltiple s h o ~ in n t h r hloclc diagram in Figure 6.19 I1 represents the sl atr-c~liiations ,234) described in C1iaptc.r 2.3.2 As betore, WP start with a, wctor x(t) witli AI illpiit sigiiids, or y(t) with Ir' output higrials and OT z(t) with N si ate variables The niatrices ot the sta pacr rrioilr t 11(xi i Ilalrc diiriensi(xis c KxM, b) I< x hl Pigtire 6.19: Block diagraru of The coaiplctc trarisft R state-space representation ( s ) f o ~this state-spacc reprc i;iinetl hy suitable maly icwt transf(>rfunctions a r i d rules lor conibining LTI-systmis step-by-sl ep Pii5t of all we recognise a par idle1 nit in Figiirti 6.19 with two componcnt systcrns with the transfcr functions 5) and H2 (s) (6.47) e transfer functions in itre direct prt.th nt From (6.42) WP know that for the liar (6.35) The coiiiporwrit transfer functioii L ( s )inr~stbe deterniiiied fiorii the lower path 11 cotisists of t hie stems i r i series (6.40) (6.I9)