🚀 go-pugleaf

In article <1992Sep30.185418.19486@noao.edu> nroddier@noao.edu (Nicolas Roddier) writes:

   From: nroddier@noao.edu (Nicolas Roddier)
   Newsgroups: sci.engr.control
   Date: 30 Sep 92 18:54:18 GMT
   Sender: news@noao.edu
   Organization: National Optical Astronomy Observatories, Tucson, AZ, USA
   Lines: 20
   Nntp-Posting-Host: gemini.tuc.noao.edu

   Hello control people!

   I'm wondering if the global asymptoticaly stability of a system can depend
   on a constant input.

   In other word, I have the system Xdot = f(x), f(0)=0 that is globally
   assympotically stable around the origin. Now, what can I say about the
   system Xdot = f(x) + C, where C is a constant vector. I would tend
   to think that the equilibrium shifts from the origin to another location
   but still has an infinitely large bassin of attraction, this true for
   linear system. How does it sound when f() is nonlinear?

   I'd appreciate any refence and comments/ideas. Thank you.

   Nick Roddier

try:  Xdot = -tanh(x)  [or any other f(x) bounded and so that xf(x)<0], dim=1.
Add a big constant and everything goes off to infinity.
By the way, there is lot being written nowadays about such issues (in less
trivial cases)... look under "input to state stability", "BIBO stability"...
in SCL, IEEE/TAC, MCSS...
-- 
Eduardo D. Sontag
Department of Mathematics
Rutgers Center for Systems and Control (SYCON)
Rutgers University
New Brunswick, NJ 08903, USA

(Phone: (908)932-3072; dept.: (908)932-2390, FAX: (908)932-5530)
sontag@hilbert.rutgers.edu