The famous Lyapunov theory says if a system matrix $A$ is stable, then the Lyapunov inequality $$A^TP+PA<0, \qquad P>0$$ is unique which depends on the negative definite matrix $-Q$, which I didn’t write in the inequality above. Given a stable matrix $A$, is it true that $A^TP+PA<0$ for all matrices $P>0$?
2026-03-25 09:15:39.1774430139
The Lyapunov inequality for a given matrix $P$
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