If all the eigenvalues of a real matrix 
have real parts, then to an arbitrary negative definite
quadratic form 
with 
there corresponds a positive definite quadratic form 
such that if one takes
 |
then 
and 
satisfy
 |
Lyapunov's Second Theorem
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References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1122, 2000.Referenced on Wolfram|Alpha
Lyapunov's Second TheoremCite this as:
Weisstein, Eric W. "Lyapunov's Second Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LyapunovsSecondTheorem.html