Fal!2001 16.3121-1 Multivariable Frequency Response In the MIMO case, the system G(s)is described by a p m trans fer function matrix (TFM) Still have that =C(sI-A)B+D But G(s)A, B, C, D MUCH less obvious than in SISO case Discussion of poles and zeros of mimo systems also much more complicated e In siso case we use the bode plot to develop a measure of the system“size Given z=Gu, where G(jw)=G (jw) lejo(u) Then w=lejwit+)applied to G(jw)lejo(u)yields lullGGwn)lej(ant++o(w1)=I Amplification and phase shift of the input signal obvious in the SISO case ● MIMO extension? Is the response of the system large or small? /s0 010Fall 2001 16.31 21—1 Multivariable Frequency Response • In the MIMO case, the system G(s) is described by a p×m trans￾fer function matrix (TFM) — Still have that G(s) = C(sI − A) −1B + D — But G(s) → A, B, C, D MUCH less obvious than in SISO case. — Discussion of poles and zeros of MIMO systems also much more complicated. • In SISO case we use the Bode plot to develop a measure of the system “size”. — Given z = Gw, where G(jω) = |G(jω)|ejφ(w) — Then w = |w|ej(ω1t+ψ) applied to |G(jω)|ejφ(w) yields |w||G(jω1)|ej(ω1t+ψ+φ(ω1)) = |z|ej(ω1t+ψo) ≡ z — Amplification and phase shift of the input signal obvious in the SISO case. • MIMO extension? — Is the response of the system large or small? G(s) = ∙ 103/s 0 0 10−3/s ¸