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Article #8Lyapunov Stability
From: Mile Erlic
Date: Tue, 03 Nov 1992 00:43
Date: Tue, 03 Nov 1992 00:43
28 lines
1497 bytes
1497 bytes
Hello,
I have an interesting stability problem and I was wondering
whether there might be others studying this problem type. Given
a differential equation
x' = f(x(t),y(t))
y' = f(x(t),y(t))
where x',y' and x'',y'' are continuous functions we have a Lyapunov function
v = .5x^2 + .5y^2
The derivative of v is bounded by
v' <= - a*norm(x)^2 + b*norm(x)^3 = -(a-b*norm(x))*norm(x)^2
Is this system stable? Unstable? If stable, is there a way of
determining the x(0) required in order to guarantee x->0 as t->infinity?
I realize that the statements above are not veru rigourous. If there
is anybody out there studying this stuff I could then detail the problem
more thoroughly.
--
Mile Erlic, Dept. Elec. & Comp. Eng., Univ. of Victoria
Victoria, B.C., Canada V8W 3P6, (604) 721-8660
merlic@sirius.uvic.ca
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<1992Nov3.004354.12748@sol.UVic.CA>Path:
arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!cs.utexas.edu!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenetShow Full Headers
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Newsgroups: sci.math.research Path: arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!cs.utexas.edu!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet From: merlic@sol.UVic.CA (Mile Erlic) Subject: Lyapunov Stability Nntp-Posting-Host: jacob.uvic.ca Message-ID: <1992Nov3.004354.12748@sol.UVic.CA> Sender: Daniel Grayson <dan@math.uiuc.edu> X-Submissions-To: sci-math-research@uiuc.edu Organization: University of Victoria, Victoria, BC, Canada X-Administrivia-To: sci-math-research-request@uiuc.edu Approved: Daniel Grayson <dan@math.uiuc.edu> Date: Tue, 3 Nov 1992 00:43:54 GMT Keywords: Lyapunov Stability, Robotics Lines: 30