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Lyapunov Equations

Consider the following Lyapunov equation

qAssume that *A* is stable, then the
following statements hold:

• *X* =

•* X *> 0 if *Q*>0 and *X *³0 if *Q*³*0*.

• if *Q*³0, then (*Q,A*) is observable iff *X* > 0.

qProof: