Re: lsim vs. filter for simulation in Octave 2.1.50

[E. Joshua Rigler]

I'm responding to my original post.  I looked more closely at the code
for lsim, and I'm still a little confused.  When a system is passed to
the lsim function, it is transformed into state-space form (i.e.

   x(t+1) = Ax(t) + Bu(t)
     y(t) = Cx(t) + Du(t)

...) then, assuming a discrete system, the appropriate matrices are used
for the simulation according to (paraphrased):

  x = x0;
  for ii=1:n
    x = A*x + B*u(ii);
  endfor
  y = C*x + D*u;

So, in other words, the feed-through (represented by D*u) is never
actually incorporated into the state.  Is this as it is supposed to be? 
If so, how does one get output analogous to the filter function from
lsim?  (The reason I want to do this, since it's probably much faster to
use Octave's filter function, is I want to have the ability to easily
implement MIMO linear predictors that may not be "strictly proper".  If
you know a better way, please let me know.)

-EJR


On Thu, 2003-10-16 at 11:30, E. Joshua Rigler wrote:
> Please, don't hesitate to tell me *why* this is a dumb question...
> 
> If I have numerator and denominator filter coefficients:
> 
>  A = [1.0  .33]
>  B = [0.2  .10]
>  lag = [0 1] ;; not necessary for anything
> 
> 
> ...or if I have a system derived from a state-space description with:
> 
> 
>  A = -.33
>  B = .10
>  C = 1
>  D = 0.2
>  sys = ss2sys (A,B,C,D,1,0,1)
> 
> 
> ...shouldn't I get the same output from:
> 
> 
>  1) filter (B,A,[1;zeros(9,1)])
> ...and...
>  2) lsim (sys,[1;zeros(9,1)],[1:10])
> 
> 
> It seems that the feedthrough term in the system structure (D*u) is not
> incorporated into the updated state properly by lsim, but maybe my
> concept of what is "proper" is flawed.
> 
> -EJR
> 
> 
> 
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Octave is freely available under the terms of the GNU GPL.

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