Fal!2001 16.3121-2 For MIMO systems, cannot just plot all of the Gi; elements of G Ignores the coupling that might exist between them So not enlightening Basic MIMo frequency response Restrict all inputs to be at the same frequency Determine how the system responds at that frequenc See how this response changes with frequency So inputs are w= wceJut, where Wc Ec Then we get z=Gs0,→2= zceu and zo∈C We need only analyze ac=G(jw)c As in the siso case, we need a way to establish if the system re- sponse is large or small How much amplification we can get with a bounded input Consider 2c=G(w wc and set lwcll2=whC 1. What can we say about the - Answer depends on w and on the direction of the input wc Best found using singular valuesFall 2001 16.31 21—2 • For MIMO systems, cannot just plot all of the Gij elements of G — Ignores the coupling that might exist between them. — So not enlightening. • Basic MIMO frequency response: — Restrict all inputs to be at the same frequency — Determine how the system responds at that frequency — See how this response changes with frequency • So inputs are w = wcejωt , where wc ∈ Cm — Then we get z = G(s)|s=jω w, ⇒ z = zcejωt and zc ∈ Cp — We need only analyze zc = G(jω)wc • As in the SISO case, we need a way to establish if the system re￾sponse is large or small. — How much amplification we can get with a bounded input. • Consider zc = G(jω)wc and set kwck2 = pwc Hwc ≤ 1. What can we say about the kzck2? — Answer depends on ω and on the direction of the input wc — Best found using singular values