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aldar and the liccevdshrllte acabsiyIds ali dci+ eCL n=de-nI a A4 (4.68) As described in Section 4.1.2, the st ability of the closed loop system is determined by the of the characteristic poly nomial ocL+). To reach a Ny quist-similar'expression, cl-n) be expressed in terms of the open loop transfer matrix m n)K-n) To that end, the eAv PNfeeFte matrix F-n)is introduced as F (4.69) Moreover, the following lemma, which is presented without a proof, will be instrument al LImma 4. 1(Schur's formula for block partitioned ditirminants) Ie4l Cvle s1- 4anP ye SL 44dReMlo n PP zreP, 4e Nees aFIf4d P HPyeeSecceMlo de-P=de-Pll de-P22 a P21 Pi P12), SctalaMie-Pl1 b0 (4.71) d de-p=de-P22 de-Pu a Pi2 Pr p2), Sctalevie-P22b0 472) Now, write the determinant of the return difference matrix Fn)as de-F+)=de+crIa lBr+ DI With the following variable substitutions P Ar P1 =a cr P21= bl P22=I+Dr (475) the right hand side of(4.73) corresponds to the last term of the right hand side of (4.71) Thus, multiplying by de-Pil= de nI a al gives r a de nI a al de+ Dr+cEnl a Albr=de acr I+ Dr 476) r a nia ar Br AD cr I+Dr Once again, applying Schur's formula, it can be shown that r a de- a a BrDr--de-ae-h-oraBrI +Dr ' "-2! 6 "#( = = % % % . % " " "-3! & ( ) & ( # # # # # # "15! % # # # # ## # # "1#! # # # ## # # "1(! B % " " "1,! < # # "1"! # # "1/! "1,! "1#! # "1-! " "11! = "12! "13!