Fal!2001 16.3120-9 By geometry, we need to test if LpG)- LNg)<d(w)= 1+ LNga)l a But Lp= Ln(1+E) LN=LN E e So we must test whether LN E <1+LN Vw LN E<1 +L Recall that T(s, l(s/(1+L(s)) TN(ju)E(ju)=|TNj)·|E(ju)≤|N(ju)·|Eo(ju) So the test for robust stability is to determine whether TN(ju)·|Eoi)<1uFall 2001 16.31 20—9 • By geometry, we need to test if: |Lp(jω) − LN(jω)| < |d(jω)| = |1 + LN(jω)| ∀ω • But Lp = LN(1 + E) ⇒ Lp − LN = LN E • So we must test whether |LN E| < |1 + LN| ∀ω or ¯ ¯ ¯ LN ¯ ¯ E¯ ¯ < 1 ¯1 + LN • Recall that T(s) , L(s)/(1 + L(s)) |TN(jω) E(jω)| = |TN(jω)| · |E(jω)| ≤ |TN(jω)|·|E0(jω)| • So the test for robust stability is to determine whether |TN(jω)|·|E0(jω)| < 1 ∀ω