Consider the system x (t) * (t) and the performance measure = J = = x (t) 4x(t) + 4x(t) + u(t) = [20x (1) + 5x2 (1) + u(1)]dt 0 ) (a) Find the eigenvalues of the open-loop system (Hint: x = Ax+ Bu. Consider u = 0 and find the eigenvalues of A). (b) Find the optimal control law u* (t). ) (c) Find the eigenvalues of the closed-loop system. Comment on the change of the eigenvalues compared with the open-loop case. (Hint: x = Ax + Bu with u = Kx. Find the eigenvalues of A + BK.)