Fall 2001 16.3110-11 Note that the transfer function matriz(TFM) notion is a MIMO general ization of the siso transfer function It is a matrix of transfer functions gn1(s)…g1m(s) G(s) where gii(s)relates the input of actuator j to the output of sensor i · Example 0 1s-2 2s+2 It is relatively easy to go from a state-space model to a TFM, but not obvious how to go back the other way. e Note: we have to be careful how to analyze these TFms Just looking at the individual transfer functions is not useful Need to look at the system as a whole will develop a new tool based on the singular values of G(sFall 2001 16.31 10–11 • Note that the transfer function matrix (TFM) notion is a MIMO general￾ization of the SISO transfer function – It is a matrix of transfer functions G(s) =   g11(s) ··· g1m(s) ... gp1(s) ··· gpm(s)   – where gij (s) relates the input of actuator j to the output of sensor i. • Example: G(s) =      1 s + 1 0 1 s − 2 s − 2 s + 2      • It is relatively easy to go from a state-space model to a TFM, but not obvious how to go back the other way. • Note: we have to be careful how to analyze these TFM’s. – Just looking at the individual transfer functions is not useful. – Need to look at the system as a whole – will develop a new tool based on the singular values of G(s)