Problem 3. (40 points) Consider a system given by the state-space form x=Ax+Buy=Cx+Du where the state matrices are given by A=[5310],B=[11],C=[11],D=0 1) (8 points) Write the transfer function G(s)=Y(s)/U(s) for the system. 2) (8 points) Determine if it is possible to assign arbitrary pole locations for the system. 3) (12 points) Find the transformation T so that if z=Tx, the state matrices describing the dynamics of z are in controller canonical form (CCF). Compute the new matrices A,B,C,D. 4) (12 points) Design a state feedback controller u=Kx that satisfies the following specifications: damping ratio =0.707, and step-response peak time is under 3.14sec. (Hint: If you do the control design in CCF, remember to convert the control law back to the original coordinates x.)