13.1 Conformal Mapping: Cauchy's Theorem (保角映射:柯西定理) Recall Stability Problem: To determine the relative stability of a closed-loop system we must investigate the characteristic equation of the system 1+GH(s)=0 Where GH(S)or 1+ GH(s)is a complex function of s, and the difference between GH(s) and 1+ GH(s) is only 1. So (1)We can investigate 1+ GH(s) through GH(S) (2)How to investigate GH(S)?----If s has a variation, then GH(s) has a variation certainly. We can suppose the variation of s, to see the change of GH(S)13.1 Conformal Mapping: Cauchy’s Theorem ( 保角映射: 柯西定理 ) Recall Stability Problem: To determine the relative stability of a closed-loop system, we must investigate the characteristic equation of the system: 1+ GH(s) = 0 Where GH(s) or 1+ GH(s) is a complex function of s , and the difference between GH(s) and 1+ GH(s) is only 1. So (1) We can investigate 1+ GH(s) through GH(s) ; (2) How to investigate GH(s) ? ---- If s has a variation , then GH(s) has a variation certainly. We can suppose the variation of s, to see the change of GH(s)