(Local linearization around equilibrium: nonlinear input). Consider the nonlinear system y y y = u2 1. (a) Compute a state-space representation for the system with input u and output y. Write the model in the form x = f (x, u) y = g (x, u) for appropriate functions f and g . (b) Linearize the system around the solution y(t) = 0, u(t) = 1, t 0