A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

The zero, input response of a system given by the state space equation $$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ \bullet }}} \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]and\left[ {\matrix{ {{x_1}} & {\left( 0 \right)} \cr {{x_2}} & {\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr } } \right]is$$$

The number of distinct Boolean expressions of 4 variables is

If the functions W, X, Y and Z are as follows

W= R+$$\overline P Q + \overline R $$ S
X = $$X = PQ\overline R \,\overline S + \overline P \,\overline Q \,\overline R \,\overline S + P\overline Q \,\overline R \,\overline S $$
Y = $$RS + \overline {OR + P\overline Q + \overline {PQ} } $$
Z = $$R + S + \overline {PQ + \overline {PQR} + P\overline {QS} } $$