$3\mathrm{.}21$ Find the transfer functions for the block diagrams in Fig. $3\mathrm{.}51,$ using the ideas of block$-$diagram simplification. The special structure in Fig. $3\mathrm{.}51($b$)$ is called the "observer canonical form" and will be discussed in Chapter $7.$

$($a$)$

$($b$)$

$($c$)$

Figure $3\mathrm{.}51$

Block diagrams for Problem $3\mathrm{.}21$