Lyapunov's Second Theorem

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite quadratic form (x,Vx) such that if one takes


then (x,Vx) and (x,Wx) satisfy


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Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1122, 2000.

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Lyapunov's Second Theorem

Cite this as:

Weisstein, Eric W. "Lyapunov's Second Theorem." From MathWorld--A Wolfram Web Resource.

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