A simple robot manipulator has been modelled within a state-space model with the following matrices 1 A= [] B=[] L -6 -51 (a) (b) (c) (d) x = Ax + Bu y = Cx + Du C = [2 1] D=0 Obtain the transfer function for the above plant. Note, that the transfer function is C(sI-A) B+D, where I is the identity matrix. [8] From the transfer function obtained in part (a), determine its discrete-time transfer form, G(z). Note that the transfer function of a zero-order hold (z.o.h.) is (1-e-Ts)/s. [8] Also obtain the discrete-time transfer function for a sampling period 0.5 seconds. [1] Determine the poles of the transfer function G(z) obtained in part (c) and then position them on the Z plane. Determine the system stability. [3]