Since the sequence is bounded below by *X**i* > *X*. Hence the limit

exists and is hermitian, and we have *X**+ **³** **X*. Passing the limit *n**®¥** *in (0.9), we get *Q**(X**+**)=*0. So *X**+* is a solution of
(0.7).

Note that *X**+ **-X **³** 0 *and*
*

Hence, *X**+ **-X>0 *and *A**+**=A+BB*X **+** *is antistable.