[] A continuous time system is described by dx, dt dx, dt =-2x + x +U...

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[] A continuous time system is described by dx, dt dx, dt =-2x + x +U = = x - 2x +u a. Show that this system is not controllable but stabilizable. b. Obtain the closed loop characteristic equation when the system is under state feedback control, i.e. u(t) = -kx (t)-kx (t). Show that the feedback control law that will assign the controllable eigenvalue to -c (c>0) is not unique. [] A continuous time system is described by dx, dt dx, dt =-2x + x +U = = x - 2x +u a. Show that this system is not controllable but stabilizable. b. Obtain the closed loop characteristic equation when the system is under state feedback control, i.e. u(t) = -kx (t)-kx (t). Show that the feedback control law that will assign the controllable eigenvalue to -c (c>0) is not unique.