Re: Simultaneous stabalization - basic questions

Hi Zdenek,

Ok thanks for your reply. Yes, i agree if the family of plants
considered are all stable, then the solution is trivial. In fact K
doesnt have to be zero, but as long as it satisfies the small gain
theorem for the 'worst' plant. But of course it still trivially
exists.

I wonder if it is still trivial if some degree of performance is
guarenteed as well as stability (e.g. zero offset)?

Initially i found the problem of Simultaneous stabalization confusing
because i didnt see the difference between robust stabalization and
Simultaneous stabalization. But it is clearer now.
Jon




Zdenek Hurak <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> Hi Jon,
> 
> J. wrote:
> > 1) Do the plants being stabalized HAVE to include non-stable plants?
> 
> Obiously yes, what would you stabilize here if everything were stable?
> 
> > Is it meaningful to prove a controller exists which stabalizes a
> > finite number of stable plants?
> 
> No. Because such a controller is ALWAYS GUARANTEED TO EXIST. Just consider a 
> controller described by C(s) = 0 ...
> 
> You are done with the proof.
>  
> > 2) Strong stabalization means the controller has to be stable too. Is
> > this a necessary condition for the  Simultaneous stabalization
> > solution? I mean if one can find a controller which stabalizes a
> > finite number of plants, does the controller HAVE to be stable? Or is
> > it ok to just find any controller which stabalizes the plants?
> 
> No. If you task is to find a controller, that stabilizes (simultaneously) 
> several plants, then you are obviously happy if the controller just 
> stabilizes (simultaneously) several plants...
> 
> If you need a STABLE controller that stabilizes (simultaneously) several 
> plants, then you are obviously happy if the controller stabilizes 
> (simultaneously) several plants and is itself stable...
> 
> Quite simple... Don't let definitions and formulas prevent you from simple 
> thinking. 
> 
> 
> Zdenek