State-Space Linearization

Jacobian Computation

For nonlinear dynamics dx/dt = f(x, u), linearize around (x_ref, u_ref):

A = ∂f/∂x |_{x_ref}  (n×n matrix)
B = ∂f/∂u |_{x_ref}  (n×m matrix)

Discretization

For discrete-time control with timestep dt: