3. (20 points) Consider the two-input nonlinear system (if) f=e" -1 T=1u Y= Use the center manifold theory to prove that the two-input system is locally asymptotically stabi- lizable by u=z+ az? { v=y+ B3 with suitable coefficients and S. Hint: Take advantage of the property of an exponential function. Use the adding an integrator technique to design a smooth state feedback control law u = u(z,z,y), v=1(z,2,Y), with (0,0,0) = 0 and v(0,0,0) = 0, globally asymptotically stabilizing the system. Hint: Observe that, for instance, the virtual controller = z y*:ZZ globally asymptotically stabilizes the z-subsystem