Problem 4. A second order system is described by da(t) = x(t), dt dx (t) dt 4r(t) 5x2(t) +u(t), y(t)=2x(t)+22(t) x (0) = 10; x2(0) = x20 = Find the relation between Y(s) and U(s), 10, T20 in the transform (Laplace) domain. Find pole(s) and zero(s) of the input output transfer function. For u(t) ezt, where z is a zero of the transfer function, show that y(t) = 0 is possible by properly selecting the initial conditions for the system state variables. This implies that the plant zeros block transmission of certain input signals to the output. =