Re: Directions in MIMO systems

Dear Matthias Heller,

Thank you very much for your email.

>1.) On page 78, MIMO bandwidth, you call the direction associated with
sigma_max(S) the worst case or low gain direction.

What we mean (and I agree it is a bit confusing) is that the direction of
the loop trasnfer function L has its low gain direction, and this then
translates into the "worst" direction of S=(I+L)^-1, corresponding
to sigma_max(S).

>2.) Directions of MIMO-Systems

The message is that in MIMO systems everything has directions:
the gain (as expressed by the singukar values); the poles; the zeros -
an these directions are in generqal not related.

> C*vi = Output direction where where vi = right eigenvector

Yes, this is the same as our output pole vector

>they call z_i = KC*vi the Input directions where K=Controller Matrix

?? I am not sure what his is. It is not a property of the plant only, but
also of the controller

>wi'*B = input direction where wi=left eigenvector, B= Input Matrix

Yes, this is the same as our input pole vector

> r_i = wi'*B*K = is called output direction

?? Again I am not sure what this is

>Is there any literature where the definition of directions is detailed
explained?

There does not seem to be very much.
An approach similar to ours with respoect to pole and zero directions
is given by Douglas and Athans (1995) (In their chapter on
"Multivariable poles, zeros and pole-zero cancellations
in "The Control Handbook", 30th Ed., CRC Press, pp. 445-450).

Best regards,
Sigurd Skogestad
Received on Mon Dec 21 16:06:49 1998