Fall 2001 6.31106 Note that the vi give the relative sizing of the response of each part of the state vector to the response 2()=/1 mode 1 0 0.5 t) mode 2 0.5 Clearly eit gives the time modulation Ai real - growing/decaying exponential response A i complex -growingdecaying exponential damped sinusoidal Bottom line: The locations of the eigenvalues determine the pole locations for the system, thus They determine the stability and/ or performance transient behavior of the system It is their locations that we will want to modify when we start the control workFall 2001 16.31 10–6 • Note that the vi give the relative sizing of the response of each part of the state vector to the response. v1(t) = 1 0 e−t mode 1 v2(t) = 0.5 0.5 e−3t mode 2 • Clearly eλit gives the time modulation – λi real – growing/decaying exponential response – λi complex – growing/decaying exponential damped sinusoidal • Bottom line: The locations of the eigenvalues determine the pole locations for the system, thus: – They determine the stability and/or performance & transient behavior of the system. – It is their locations that we will want to modify when we start the control work