Q.1 Consider the discrete-time process x(x+1)=1 y(k)-[01]x(k) (a) Find the range of and // such that the system is both controllable and observable. (3 Marks) (b) Assuming that the state variables are accessible, design a deadbeat state feedback controller. (7 Marks) (c) Assuming that only the output y(k) is available, design a deadbeat observer to estimate the state variables, and use these estimates to design an output-feedback controller. (7 Marks) (d) Design a two-degree-of-freedom controller such that the transfer function from the command signal, u(k), to the system output, y(k), follows the reference model, (4 Marks) (c) Assuming that there is a time-delay of 1 in the input signal, the corresponding model of the system is then *+1)= y(k)=[01]x(k) -1) What is the state of the system at time k? What is the order of the system? Justify your answers. (4 Marks)