P11.5 Consider the system described by

x(t) = Ax(t) + Bu(t), where x(t) = (x1(1), x2 (1))", 0 1 and B = 00 The state feedback of the system is u(t) = -kx (1) -k2x2 (1), where k = 3k and k = k, k > 0. Given the initial condition x (0) = (0,1)", and determine the gain k to minimize the performance index J = f (x(t)x(t) + u (t)u(t)) dt. Plot the function J(k).