Note that

Post-multiply the above
equation by *x*:

Recall that *RX**2**x* = 0, we have

(*A,R*) stabilizable Þ *X**2** x=0 *Þ *
*

(Þ )* H* Î *dom(Ric) *Þ * A+RX* is stable Þ *(A, R)* is stabilizable.