Let (T=0.5 mathrm{~s}) for the system of Fig. P5.4-4. Derive a set of discrete state equations for

Question:

Let $T=0.5 \mathrm{~s}$ for the system of Fig. P5.4-4. Derive a set of discrete state equations for the closed-loop system, for the plant described by each of the differential equations.

(a) $\frac{d y(t)}{d t}+5 y(t)=3 \bar{m}(t)$

Choose the state variable to be $y(k T)$.

(b) $\frac{d^{2} y(t)}{d t^{2}}+9 \frac{d y(t)}{d t}+8 y(t)=4 \bar{m}(t)$
Choose the state variables to be $y(k T)$ and $d y(t) /\left.d tight|_{t=k t}$.

Fig. P5.4-4.