Lyapunov Stability

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1 total messages Started by Mile Erlic Tue, 03 Nov 1992 00:43

Author: Mile Erlic
Date: Tue, 03 Nov 1992 00:43

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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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