The square matrices $A$ is invertible, $Q$ and $G$ symmetric positive semidefinite. Moreover, $(A,G)$ is controllable, and $(Q,A)$ is observable. I have the following question
- Is $(-A,-G)$ controllable?
- Is $(-Q,-A)$ observable?
Thanks in advance!
2026-03-28 08:47:48.1774687668
Controllable and observable
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By the Kalman rank condition, multiplying the matrices by a constant factor does not influence controllability (and observability).