Adapted from $[$Am$]17\mathrm{.}80$: Consider the system comprised of three subsystems in cascade:

H$1($z$)$ H$2($z$)$ H$3($z$)$

x$[$n$]$ y$[$n$]$

It is known that h$1[$n$]=0\mathrm{.}5(0\mathrm{.}4)$nu$[$n$],$ H$2($z$)=$ A$($z$+$$)$

z$+$ $,$ and h$3[$n$]=$ d$[$n$]+0\mathrm{.}5$d$[$n $1].$ Choose A$,$ $,$

and such that when all subsystems are relaxed, y$[$n$]=$ x$[$n$].$ For the parameters you choose, are all of

the subsystems stable? Is the system as a whole stable?