Talk:Lyapunov equation

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[edit] Weak Lyapunov First theorem

Does it exist a weak formulation for that theorem?

I need the proof that


Theorem. If there exist

P >= 0 and Q > 0 satisfying A^T P + PA + Q = 0 then the linear system is globally Lyapunov stable

. The quadratic function V(z) = z^T Pz is a Lyapunov function that can be used to verify stability.

Or also (if possible, I have no idea about the proof of the theorem)

Theorem. If there exist

P >= 0 and Q >= 0

satisfying A^T P + PA + Q = 0 then the linear system is globally

Lyapunov stable

. The quadratic function V(z) = z^T Pz is a Lyapunov function that can be used to verify stability.


194.206.211.87 08:59, 16 May 2007 (UTC)