Suppose I have the equation $$A^\top K +KA+Q=0$$ I know that $A$ is stable and $Q$ is symmetric. I want to prove that the solution $K$ to this equation is unique. What constraints should I put on $Q$? How can I prove the uniqueness of the solution?
2026-03-26 12:45:23.1774529123
For which matrix $Q$ does the lyapunov equation have a unique solution?
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