Fa2004 16.3339-3 Note that the vi give the relative sizing of the response of each part of the state vector to the response mode 1 0 de 2 Clearly eid gives the time modulation A i real- growing/decaying exponential response Ai 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 be- havior of the system It is their locations that we will want to modify with the controllers� � � � Fall 2004 16.333 9–3 • Note that the vi give the relative sizing of the response of each part of the state vector to the response. 1 v1(t) = e−t mode 1 0 0.5 v2(t) = e−3t mode 2 0.5 • 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 be￾havior of the system. – It is their locations that we will want to modify with the controllers